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User talk:The-writer

Welcome to Wikibooks. I hope you enjoy your time here.

Just one quick note, if I may - we don't usually create pages just to leave them blank. Instead we tend to leave red links (as are in your Backgammon main page) to indicate that nothing as yet has been written about the subject, and to encourage others to help write on the topic. All the best, Jguk 09:04, 17 June 2006 (UTC)

 * I should have added that our naming policy for new books is that they should use back-slashes for pages, not colons. (See Naming policy.) So it would be Backgammon/Introduction rather than Backgammon:Introduction. This also has the benefit of automatically creating a backlink to the Backgammon page on each other page of the book. Kind regards, Jguk 09:07, 17 June 2006 (UTC)

title: User talk:The-writer


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OpenOffice.org/Calc

OpenOffice User's Manual: OpenOffice.org Calc Adapted under license from OOoAuthors

What is Calc?
Calc is the spreadsheet component of OpenOffice.org (OOo). You can enter data, usually numerical data, in a spreadsheet and then manipulate this data to produce certain results.

Alternatively you can enter data and then use Calc in a ‘What If...’ manner by changing some of the data and observing the results without having to retype the entire spreadsheet or sheet.

Spreadsheets, sheets and cells
Calc works with elements called spreadsheets. Spreadsheets consist of a number of individual sheets, each containing a block of cells arranged in rows and columns.

These cells hold the individual elements—text, numbers, formulas etc.—which make up the data to be displayed and manipulated.

Each spreadsheet can have many sheets and each sheet can have many individual cells. In version 3.0 of OOo, each sheet can have a maximum of 65,536 rows and a maximum of 1024 columns.

You can enter data into Calc in several ways: using the keyboard, the mouse (dragging and dropping), the Fill tool, and selection lists. Calc also provides the ability to input information into multiple sheets of the same document at one time.

After entering data, you can format and display it in various ways. A function is a pre-defined calculation entered in a cell to help you analyze or manipulate data in a spreadsheet. All you have to do is add the arguments, and the calculation is automatically made for you. Functions are the main reason for spreadsheets. If you understand functions, then you can start to use the real power of a spreadsheet.

Understanding functions
Calc includes over 350 functions to help you analyze and reference data. Many of these functions are for use with numbers, but many others are used with dates and times, or even text. A function may be as simple as adding two numbers together, or finding the average of a list of numbers. Alternatively, it may be as complex as calculating the standard deviation of a sample, or a hyperbolic tangent of a number.

Typically, the name of a function is an abbreviated description of what the function does. For instance, the FV function gives the future value of an investment, while BIN2HEX converts a binary number to a hexadecimal number. By tradition, functions are entered entirely in upper case letters, although Calc will read them correctly if they are in lower or mixed case, too.

A few basic functions are also represented by symbols. For instance, SUM, which adds arguments, can also be entered as + while PRODUCTION, which multiplies arguments, can also be entered as *.

Each function has a number of arguments used in the calculations. These arguments may or may not have their own name. Your job is to enter the arguments needed to run the function. In some cases, the arguments have pre-defined choices, and you may need to refer to the online help or Appendix B (Description of Functions) in this book to understand them. More often, however, an argument is a value that you enter manually, or one already entered in a cell or range of cells on the spreadsheet. In Calc, you can enter values from other cells by typing in their name or range, or—unlike the case in some spreadsheets—by selecting cells with the mouse. Should the values in the cells change, then the result of the function is automatically updated.

Strictly speaking, when all the arguments are entered and a function is ready to run, it becomes a formula. These terms are sometimes used interchangeably, but the distinction is worth preserving, because a formula can use functions as an argument.

For compatibility, functions and their arguments in Calc have almost identical names to their counterparts in Microsoft Excel. However, both Excel and Calc have functions that the other lacks. Occasionally, too, functions with the same names in Calc and Excel have different arguments, or slightly different names for the same argument—neither of which can be imported to the other. However, perhaps nine-tenths of functions can be imported between Calc and Excel without any problems.

Understanding the structure of functions
Except for simple functions such as + or *, all functions have a similar structure. If you use the right tool for entering a function, you can escape learning this structure, but it is still worth knowing for troubleshooting.

To give a typical example, the structure of a function to find cells that match entered search criteria is:

= DCOUNT (Database;Database field;Search_criteria)

Like most functions, this one starts with an equal sign. It is followed by DCOUNT, the name of the function. After the name of the function comes its arguments. All arguments are required, unless specifically listed as optional.

Arguments are added within the brackets (parentheses) and separated by semicolons, with no space between the arguments and the semicolons. Many arguments are a number. A Calc function can take up to thirty numbers as an argument. That may not sound like much at first. However, when you realize that the number can be not only a number or a single cell, but also an array or range of cells that contain several or even hundreds of cells, then the apparent limitation vanishes.

Other arguments may be a column label, a mathematical constant, or a value unique to that function.

Depending on the function, arguments may have to be entered with straight quotation marks. However, this requirement is not consistent. Otherwise similar formulas may differ only in this requirement, and no simple rule tells you which is which. You simply have to know or check the requirements in the online help.

The only exception to these structural rules are basic arithmetical functions entered with symbols. For example, instead of entering =SUM(2;3), you can enter =2+3.

Advanced structure
As well as being used on its own, a function can be an argument in a larger formula. A formula, however, is limited by the fact that it can only do one function at a time. You need to make sure that functions are done in the right order if the formula is going to work.

To help set the order for functions in a multiple-function formula, you use parentheses within parentheses. When the formula is run, Calc does the innermost function first, then works outwards. For example, in the simple calculation =2+(5*7), Calc multiples 5 by 7 first. Only then is 2 added to the result to get 37.

The placement of functions within sets of parentheses is called nesting. Basically, nesting reduces a function that could run on its own to an argument in the formula. For example, in =2+(5*7), the formula (5*7) is nested within the larger formula of =2+(5*7). In other words, the nested function becomes an argument of another function.

This relation is more obvious when doing a calculation using a function with a name. For all purposes,

=SUM(2;PRODUCT(5;7))

is the same formula as =2+(5*7). However, when SUM and PRODUCT are used, then the relation is clearer. The fact that the PRODUCT function comes after a semicolon and in a set of parentheses for the SUM function makes it clear that PRODUCT is an argument for SUM. In addition, the fact that the inner pair of parentheses is around (5;7) makes clear that this operation is done before the one defined by the outer pair of parentheses.

To get an idea of what nested functions can do, imagine that you are designing a self-directed learning module. During the module, students do three quizzes, and enter the results in cells A1, A2, and A3. In A4, you can create a nested formula that begins by averaging the results of the quizzes with the formula =AVERAGE(A1:A3). The formula then uses the IF function to give the student feedback that depends upon the average grade on the quizzes. The entire formula would read:

=IF(AVERAGE(A1:A3) >85; "Congratulations! You are ready to advance to the next module"; "Failed. Please review the material again. If necessary, contact your instructor for help")

Depending on the average, the student would receive the message for either congratulations or failure.

Notice that the nested formula for the average does not require its own equal sign. The one at the start of the equation is enough for both formulas.

If you are new to spreadsheets, the best way to think of functions is as a scripting language. We've used simple examples to explain more clearly, but, through nesting of functions, a Calc formula can quickly become complex.

Formulas
See the more specific section: /Formulas/.

The database (preconditions)
The basis for work with the DataPilot is always a list with your data in raw format. Such a list is comparable to a database table. The table consists of rows (data sets) and columns (data fields). The field names are in the first row above the list.

Later we will explain that the data source could be an external file or database. The simplest use case is that your data is contained in a Calc spreadsheet. For such a list, Calc offers sorting functions that do not depend on the DataPilot.

For processing data in lists, the program must know in which area of the spreadsheet the table is. A Calc table can be anywhere in the sheet, in any position. It is also possible, that a spreadsheet contains several unrelated tables.

Calc recognizes your lists automatically. It uses the following logic:

Starting from the cell you’ve selected (which must be within your list), Calc checks the surrounding cells in all 4 directions (left, right, above, below). The border is recognized if the program discovers an empty row or column, or if it hits the left or upper border of the spreadsheet.

This means that the described functions can only work correctly if there are no empty rows or columns in your list. Avoid empty lines (for example for formatting). You can format your list by using cell formats.

If you select more than one single cell before you start sorting, filtering or calling the DataPilot, then the automatic list recognition is switched off. Calc assumes that the list matches exactly the cells you have selected. This might be useful in only very few cases.

A relatively big source for errors is that you might declare a list by mistake and you sort your list. If you select multiple cells (for example, a whole column) then the sorting mixes up the data that should be together in one row.

In addition to these formal aspects, the logical structure of your table is very important for using the DataPilot.

When entering the data, do not add outlines, groups. or summaries. This becomes clear when we think about what we could have done wrong in our Sales list example. This will give you a list of bad ideas, that you can find very often among spreadsheet users who are not informed about the possibilities of processing lists within a spreadsheet.

First bad idea: You could have made several sheets. For example, you could have made a sheet for each group of articles. Analyses are then only possible within each group. Analyses for several groups would then be a lot of hassle.

Second bad idea: In the turnover list, instead of only one column for the amount, you could have made a column for the amounts for each employee. The amounts than had to be entered into the appropriate column. An analysis with the DataPilot would not be possible any more. In contrast, one result of the DataPilot is that you can get results for each employee if you have entered everything in one column.

Third bad idea: You could have entered the amounts in chronological order. At the end of each month you could have made a sum. In this case, a sorting of the list for different criteria is not possible, and you could not use the DataPilot. The rows with the sums would be treated by the DataPilot like any other amount you have entered. Getting monthly results is one of the very fast and easy features of the DataPilot.

You start the DataPilot with Data > DataPilot > Start. If the list to be analyzed is in a spreadsheet table, select one cell within this list. Calc recognizes and selects the list automatically for use with the DataPilot.

Data Analysis
Once you are familiar with functions and formulas, the next step is to learn how to automate the processes and perform useful analyses of the data.

Calc includes several tools to help you manipulate functions and formulas, ranging from features for copying and reusing data, to creating subtotals automatically, to varying information to help you find the answers you need. These tools are divided between the Tools and Data menus.

If you are a newcomer to spreadsheets, these tools can be overwhelming at first. However, they become simpler if you remember that they all depend on input from either a cell or a range of cells that contain the data with which you are working.

You can always enter the cells or range manually, but in many cases, you can also use the Shrink/Maximize icon beside a field to change temporarily the size of the tool’s window while you select the cells with the mouse. Sometimes, you may have to experiment with which data goes into one field, but, once you have found out, the rest is simply setting a selection of options, many of which can be ignored in any given case. Just keep the basic purpose of each tool in mind, and you should have little trouble with Calc’s function tools.

You don’t need to learn them, especially if your spreadsheet use is simple, but as your manipulation of data becomes more sophisticated, they can save time in making calculations, especially as you start to deal with hypothetical situations. Just as importantly, they can allow you to preserve your work and to share it with other people—or yourself at a later session.

Subtotal
SUBTOTAL is a function listed under the Mathematical category when you use the Function Wizard (Insert > Function). Because of its usefulness, the function has a graphical interface accessible from Data > Subtotals.

As the name suggests, SUBTOTAL totals data arranged in a array—that is, a group of cells with labels for columns and/or rows. Using the Subtotals dialog, you can select arrays, then choose a statistical function to apply to them. For efficiency, you can choose up to three groups of arrays to which to apply a function. When you click OK, Calc adds subtotals and grand totals to the selected arrays, using the Result and Result2 cell styles for them.

To insert subtotal values into a sheet:

 * 1) Ensure that the columns have labels.
 * 2) Select the range of cells that you want to calculate subtotals for, and then choose Data > Subtotals.
 * 3) In the Subtotals dialog, in the Group by box, select the column that you want to add the subtotals to. If the contents of the selected column change, the subtotals are automatically recalculated.
 * 4) In the Calculate subtotals for box, select the columns containing the values that you want to subtotal.
 * 5) In the Use function box, select the function that you want to use to calculate the subtotals.
 * 6) Click OK.

If you use more than one group, then you can also arrange the subtotals according to choices made on the dialog’s Options page, including ascending and descending order or using one of the predefined custom sorts defined in Tools > Options > OpenOffice.org Calc > Sort Lists.

Scenarios
Scenarios are a tool to test “what-if” questions. Use Tools > Scenarios to enter variable contents—scenarios—in the same cell. Each scenario is named, and can be edited and formatted separately, and chosen from a drop-down list in the Navigator and the title bar of the scenario. When you print the spreadsheet, only the contents of the currently active scenario is printed.

By adding a scenario, you can quickly change the arguments of a formula and view the new results. For example, if you wanted to calculate different interest rates on an investment, you could add a scenario for each interest rate, and quickly view the results. If you had another formula that calculated your yearly income and included the result of the interest rate formula as an argument, it would also be updated. If all your sources of incomes used scenarios, you could efficiently build a complex model of your possible income.

Creating scenarios
To create a scenario, select all the cells that provide the data for the scenario.

 Select the cells that contain the values that will change between scenarios. To select multiple cells, hold down the Ctrl key as you click each cell. Choose Tools > Scenarios. On the Create Scenario dialog, enter a name for the new scenario. It’s best to use a name that clearly identifies the scenario, not the default name as shown in the illustration. This name is displayed in the Navigator and on the title bar of the scenario on the sheet itself.

Optionally add some information to the Comment box. The example shows the default comment. This information is displayed in the Navigator when you click the Scenarios icon and select the desired scenario. Optionally select or deselect the options in the Settings section. See below for more information about these options. Click OK to close the dialog. The new scenario is automatically activated.

Settings
The lower portion of the Create Scenario dialog contains several options. In most cases the default settings (shown selected in the example) are suitable.

Display border

Highlights the scenario in your table with a border. The color for the border is specified in the field to the right of this option. The border has a title bar displaying the name of the last scenario. The button on the right of the scenario border offers you an overview of all the scenarios in this area, if several have been defined. You can choose any of the scenarios from this list without restrictions.

Copy back

Copies the values of cells that you change into the active scenario. If you do not select this option, the scenario is not changed when you change cell values. The behavior of the Copy back setting depends on the cell protection, the sheet protection, and the Prevent changes settings.

Copy entire sheet

Copies the entire sheet into an additional scenario sheet.

Prevent changes

Prevents changes to the active scenario.

 * You can only change the scenario properties if the Prevent changes option is not selected and if the sheet is not protected.
 * You can only edit cell values if the Prevent changes option is selected, if the Copy back option is not selected, and if the cells are not protected.
 * You can only change scenario cell values and write them back into the scenario if the Prevent changes option is not selected, if the Copy back option is selected, and if the cells are not protected.

Working with scenarios using the Navigator
After scenarios are added to a spreadsheet, you can jump to a particular scenario by using the Navigator, then selecting a scenario from the list. You can also color code scenarios to make them easier to distinguish from one another.

To select a scenario in the Navigator, click the Scenarios icon in the Navigator. The defined scenarios are listed, with the comments that were entered when the scenarios were created.

Double-click a scenario name in the Navigator to apply that scenario to the current sheet.

To delete a scenario, right-click the name in the Navigator and choose Delete.

To edit a scenario, including its name and comments, right-click the name in the Navigator and choose Properties. The Edit Properties dialog is the same as the Create Scenario dialog.

To learn which values in the scenario affect other values, choose Tools > Detective > Trace Dependents. Arrows point to the cells that are directly dependent on the current cell.

Goalseeking
Tools > Goal Seek reverses the usual order for a formula. Usually, you run a formula to get the result when certain arguments are entered. By contrast, with Goal Seek, you work with a completed formula to see what values you need in an argument to get the results that you want.

To take a simple example, imagine that the Chief Financial Officer of a company is developing sales projections for each quarter of the forthcoming year. She knows what the company’s total income must be for the year to satisfy stockholders. She also has a good idea of the company’s income in the first three quarters, because of the contracts that are already signed. For the fourth quarter, however, no definite income is available. So how much must the company earn in Q4 to reach its goal? To answer, the CFO enters the projected earnings for each of the other three quarters and the projection for the entire year. Then she runs a goal seek on the cell for Q4 sales, and receives her answer.

Other uses of goal seek may be more complicated, but the method remains the same. To run a goal seek, at least one of the values for an argument must be a referenced cell or range. Only one argument can be altered in a single goal seek. After you get the result of a goal seek, you can replace the original value in the referenced cell with the result, or record the result elsewhere for later use, possibly as a scenario.

With the help of Goal Seek you can calculate a value that, as part of a formula, leads to the result you specify for the formula. You thus define the formula with several fixed values and one variable value and the result of the formula.

Goal Seek example
To calculate annual interest (I), create a table with the values for the capital (C), number of years (n), and interest rate (i). The formula is I = C*n*i.

Let us assume that the interest rate i of 7.5% and the number of years n (1) will remain constant. However, you want to know how much the investment capital C would have to be modified in order to attain a particular return I. For this example, calculate how much capital C would be required if you want an annual return of $15,000.

Enter each of the values for Capital C (an arbitrary value like $100,000), number of years n (1), and interest rate i (7.5%) in one cell each. Enter the formula to calculate the interest I in another cell. Instead of C, n, and i use the reference to the cell with the corresponding value. In our example, these are B1, B2, and B3.

Solver
Tools > Solver amounts to a more elaborate form of Goal Seek. The difference is that the Solver deals with equations with multiple unknown variables. It is specifically designed to minimize or maximize the result according to a set of rules that you define.

Each of these rules sets up whether an argument in the formula should be greater than, lesser than, or equal to the figure you enter. If you want the argument to remain unchanged, you enter a rule that the cell that contains it should be equal to its current entry. For arguments that you would like to change, you need to add two rules to define a range of possible values: the limiting conditions. For example, you can set the constraint that one of the variables or cells must not be bigger than another variable, or not bigger than a given value. You can also define the constraint that one or more variables must be integers (values without decimals), or binary values (where only 0 and 1 are allowed).

Once you have finished setting up the rules, you can adjust the argument and the results by clicking the Solve button.  Place the cursor in the formula cell (the cell containing the interest I), and choose Tools > Goal Seek. <li>On the Goal Seek dialog, the correct cell is already entered in the Formula cell field.</li> <li>Place the cursor in the Variable cell field. In the sheet, click in the cell that contains the value to be changed, in this example it is the cell with the capital value C.</li> <li>Enter the desired result of the formula in the Target value field. In this example, the value is 15000. The figure below shows the cells and fields.</li>

<li>Click OK. A dialog appears informing you that the Goal Seek was successful. Click Yes to enter the result in the cell with the variable value. The result is shown below.</li>

</ol>

Sharing
You can use several methods to keep track of changes you or others made to a document.

 * Use change marks to show added or deleted material and changed formatting. Later, you or another person can review and accept or reject each change.
 * Make changes to a copy of the document (stored in a different folder, under a different name, or both), then use Calc to compare the files and show the changes.
 * Save versions that are stored as part of the original file.

Reviewers can leave notes in the document or make comments attached to specific changes.

Preparing a document for review (optional)
When you send a document to someone else to review or edit, you may want to prepare it first so that the editor or reviewer does not have to remember to turn on the revision marks. After you have protected the document, any user must enter the correct password in order to turn off the function or accept or reject changes.

 * 1) Open the document and make sure that the Edit > Changes > Record menu item has a check mark next to it, indicating that change recording is active.
 * 2) (Optional) Click Edit > Changes > Protect Records. On the Protect Records dialog, type a password (twice) and click OK.

Identifying copies of spreadsheets
When sharing documents, it is important to keep track of the different copies of the document. This can be done either in the file name or in the file title. If you have not provided a file title in the spreadsheet’s properties, the spreadsheet’s filename is displayed in the title bar. To set the title of the spreadsheet, select File > Properties > Description.

Cells
You have to protect the sheet first.To protect cells go to Format > Cells > Cell protection.

Macros
A macro is a saved sequence of commands or keystrokes that are stored for later use. An example of a simple macro is one that “types” your address. The OpenOffice.org (OOo) macro language is very flexible, allowing automation of both simple and complex tasks. Macros are especially useful to repeat a task the same way over and over again. Macros can be in many different languages, but the default is BASIC. This section briefly discusses common problems related to macro programming using Calc.

The following steps create a macro that performs paste special with multiply.

<ol> <li>Open a new spreadsheet.</li> <li>Enter numbers into a sheet.</li>

<li>Select cell A3, which contains the number 3, and copy the value to the clipboard.</li> <li>Select the range A1:C3.</li> <li>Use Tools > Macros > Record Macro to start the macro recorder. The Record Macro dialog is displayed with a stop recording button.</li>

<li>Use Edit > Paste Special to open the Paste Special dialog.</li>

<li>Set the operation to Multiply and click OK. The cells are now multiplied by 3.</li>

<li>Click Stop Recording to stop the macro recorder and save the macro.</li> <li>Select the current document. For this example, the current Calc document is Untitled. Click on the + next to the document to view the contained libraries. Prior to OOo version 3.0, new documents were created with a standard library; this is no longer true. In OOo version 3.0, the standard library is not created until the document is saved, or the library is needed. If desired, create a new library to contain the macro (but this is not necessary).</li>

<li>Click New Module to create a module in the Standard library. If no libraries exist, then the Standard library is automatically created and used.</li>

<li>Click OK to create a module named Module1.</li>

<li>Select the newly created Module1, enter the macro name PasteMultiply and click Save. The created macro is saved in Module1 of the Standard library in the Untitled2 document (see Listing 1).</li> </ol>

''Listing 1. Paste special with multiply.''

Calc can call macros as Calc functions. Use the following steps to create a simple macro:

<ol> <li>Create a new Calc document named CalcTestMacros.ods.</li> <li>Use Tools > Macros > Organize Macros > OpenOffice.org Basic to open the OpenOffice.org Basic Macros dialog. The Macro from box lists available macro library containers. My Macros contains macros that you write or add to OOo. OpenOffice.org Macros contains macros included with OOo and should not be changed. All other library containers are currently open OOo documents.</li>

<li>Click Organizer to open the OpenOffice.org Basic Macro Organizer dialog.</li>

<li>Click the Libraries tab.</li> <li>Select the document to contain the macro.</li> <li>Click New to open the New Library dialog.</li>

<li>Enter a descriptive library name (such as AuthorsCalcMacros) and click OK to create the library. The new library name is shown the library list, but the dialog may show only a portion of the name.</li>

<li>Select AuthorsCalcMacros and click Edit to edit the library. OOo automatically creates a module named Module1 and a macro named Main.</li>

<li>Modify the code so that it is the same as that shown in Listing 2. The important addition is the creation of the NumberFive function, which returns the number five. The statement Option Explicit forces all variables to be declared before they are used. If Option Explicit is omitted, variables are automatically defined at first use as type Variant.</li> </ol>

''Listing 2. Function that returns five.''

Getting Help

 * Spreadsheets with OpenOffice.org 3.x Calc - OpenOffice.org Wiki

General Spreadsheet help

 * Excel Tutorials Excel - Spreadsheet Help Spreadsheet - Tips and Tutorials
 * Excel 2003 Help and How-to - Excel - Microsoft Office Online
 * The Spreadsheet Page - By John Walkenbach
 * Excel Tutorial - By Excel Easy
 * Forums - Excel User Group
 * Excel Tips from MrExcel
 * Excel Help Forum

OpenOffice.org/ Calc es:OpenOffice.org/Calc: la hoja de cálculo OpenOffice.org Calc OpenOffice.org/Calc OpenOffice/Calc – táblázatkezelő OpenOffice.org Calc OpenOffice.org/Calc OpenOffice.org/Calc OpenOffice.org Calc ღია ოფისი (Open Office)/ნაწილი 3 Calc - ელცხრილები

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Hi, I am Tim, I am a Developer of AegeanLinux (http://www.aegeanlinux.be). I hope to be able to provide many contributions, especially on Linux, but for the moment, I think the OpenOffice.org pages need editing. After all, how can we get people to move to "Open Standards ... Open Source", if no one can even use OpenOffice?

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Mac OS X Tiger/System Preferences/Dock

When the  > Dock menu is missing an option you want, you'll have to turn to the Dock pane of System Preferences. This pane gives you more fine-grained control over the Dock.

 * Dock Size - This slider adjusts the size of the dock. You can also do this by dragging the thin line that separates the Dock into left and right sides.
 * Magnification - When Magnification is on, the icons in your Dock “bulge” as you move your cursor over them. You'll either go gaga for this effect or find it distracting. The slider next door controls just how large the icons on the Dock will become when you move your cursor over them.
 * Position on screen - This controls where the Dock is located on the screen. Most people prefer to have the Dock on the bottom, but on some small widescreen laptops, vertical space is more valuable than horizontal, and having the Dock running down the side of the screen saves a lot of space.
 * Minimize using - The Genie Effect, the default setting, makes the window minimize like a genie going into a bottle. The Scale Effect is more modest, and goes faster.
 * Animate opening applications - By default, application icons in the Dock bounce up and down while opening. Turning this option off makes the small triangle under the icon pulse instead.
 * Automatically hide and show the Dock - When this option is turned on, the Dock will disappear completely unless you let your cursor rest right next to the edge of your screen where your Dock is. The Dock will then temporarily pop out so you can work with it. When you move the cursor away, it will disappear again.

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Suomen kieli ulkomaalaisille/Sisältö/Verbityyppi 2

Type 2 Verb Characteristics

 * These verbs have monosyllable stems ending in a long vowel or a diphthong, or have longer stems ending -oi and dictionary forms ending -da or -dä which do not belong to the stem.
 * All Finnish verbs have a first infinitive (i.e. dictionary listed) form ending with the letter -a or -ä which is added to the stem. But as no Finnish verb can have 3 consecutive vowels, the infinitve -a or -ä cannot be added directly to the stem of these verbs. Instead, an intervening -d is added after the stem and before the addition of the infinitive -a or -ä. Hence this group of verbs has dictionary forms ending -da or -dä but the d is not part of the stem and only appears in the infinitive forms.

Because of the long vowel stem ending, the third person singular does not extend the last vowel again (c.f. Type 1 verbs).

Present tense
voida - to be able to  or to have the power to do or "can"

Very many of the verbs that have single syllable stems ending in a long vowel or a dipthong are in this group (e.g. saada to get, löydä to find).

But there are also some longer verbs in this group that have often been formed from nouns. For instance imuroida to vacuum clean formed from a shortened form of the word pölynimuri vacuum cleaner (literally, sucker of dust).

Formation of the simple past tense (imperfect)
The imperfect ending marker is -i- but this cannot be added directly to the stem. This is because the stem already ends in two vowels and no Finnish verb can contain three consecutive vowels.

The solution to this problem is that Type 2 verbs is as follows.

 * if the final vowel of the stem is an i then the i of the stem is dropped.
 * Thus the simple past tense form is identical to the present tense.

 * however, if the last vowel is not an i, the FIRST of the two vowels in the stem is dropped.
 * Thus the dictionary form is not always easily apparent from the past tense form, especially for the short form verbs

voida - to be able to  or to have the power to do or "can"

Syodä to eat

Distinguishing Past, Present and Future
If present tense is also used as the future tense (as it is for all Finnish verb types), and the past tense in many Type 2 verbs forms is identical to these, why is this not confusing?

This is a good question (assuming you have already been wondering about this)!!

The answer will most likely be clear from the context. For example if it may includes a time clue like the word tomorrow, next week, last week etc. But this may not be the case.

An additional clue will come in the object form following the verb. Consider the following.

1. Imuroin auton

2. Imuroin autoa

Imuroida means to vacuum clean and auto is car, but here appears in two forms. the accusative -n form and the partitive -a form. Imuroin could mean I will vacuum (future tense), or I am vacuuming (right now, present tense) or I vacuumed past tense.

If the meaning is present tense, then the phrase has to be Imuroin autoa. Because the action is ongoing, object rules dictate that the object must be in the partitive case, indicating incomplete action. However imuroin autoa could also mean that I vacuumed part of the car some time ago (but perhaps this is unlikely) or I will vacuum part of the car, but not all of it (equally unlikely). If the car has been vacuumed and completely vacuumed, then the phrase will be imuroin auton. But equally if the job has not yet been started and the meaning is in the future I will vacuum (all of the car), it will equally be imuroin auton, so one must rely on other contextual information to distinguish the meaning.

In practise, this is hardly ever a problem.

Consonant Gradation
The good news is that type 2 verbs are not affected by consonant gradation.

Some Important Irregular Verbs
There are two verbs in Type 2 that have slightly irregular forms. As often happens with irregular verbs in many languages, they are also very common verbs, so its worth spending some time looking at them and committing them to memory. Fortunately, Finnish has remarkably few irregular verbs.

TEHDÄ TO DO or TO MAKE (the same verb serves both meanings)

NÄHDÄ TO SEE

And their past tense forms are slightly different too.

TEHDÄ TO DO or TO MAKE (the same verb serves both meanings)

NÄHDÄ TO SEE

Similarity to Type 4 verbs
Type 4 verbs are similar to Type 2 verbs in that both types of verbs have stems ending in long vowels or diphthongs and conjugate for person in exactly the same way.

The big difference is that Type 4 verbs do not have the -da or -dä infinitive endings and as a result have a variety of stem forms. Due to changes in the stems type 4 verbs are much more complex and consonant gradation effects. Type 4 verbs also form the past participle and past tense forms slightly differently.

You can learn more about Type 4 verbs in the appropriate section of this book.


text: Category:Book:CRE Loaded Features

title: Category:Book:CRE Loaded Features


text: Category:Book:Constructivist Theories in Education


text:
Category:Book:C Sharp Programming

cs:Kategorie:C sharp ko:분류:C 샤프 프로그래밍

title: Category:Book:C Sharp Programming


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Talk:Algebra/ToInclude

This are lecture notes that I wrote for the University of Phoenix class on algebra. They are under the GFDL. --Roadrunner 19:54, 17 June 2006 (UTC)

Lecture 1
Let me start by talking about ferrets.

When I was in graduate school, I had an office mate who wrote her doctoral disseration on how fluids behaved in magnetic fields. The equations that she had to deal with were really long and nasty polynomial equations. She also was a ferret lover. So everytime I see a polynomial, I imagine the equation being a small furry creature.

Thinking of a polynomial as a small furry creature isn't a bad way of approaching this chapter. Basically this chapter can be entitled the care and feeding of polynomials. In this chapter, we are going to learn the different parts of these small furry equations. We are going to learn how to what happens when you feed a polynomial some numbers and lets it digest it. We are going to learn how to make these small furry polynomial do tricks (which might be useful), and finally we are going to learn how to breed polynomials. We'll put two polynomials in a cage and let them give birth to new polynomials.

This is all going to be useful because you find polynomials all over the place. Equations which describe how big something is (i.e. Length, volumes, and surface areas) tend to end up to be polynomials. Polynomials are found in equations which describe temperatures, pressures, how long it takes for a computer program to run. Just as a quick example of the use of polynomials is the Bezier curve. I draw some dots have have the computer to connect them with a line

The line that it connects them by is a third-degree polynomial. Notice that I just used a special word. What is a third-degree polynomial you might ask? Well that's what section one is about. Section 5.1 defines some terms for polynomials. Just as ferret lovers have special terms to describe different types and different parts of ferrets, polynomial lovers have different words to describe different types and different parts of polynomials.

The next section is on adding polynomials. Why would you want to add polynomials? Well lets take a trip to the carnival and buy some ice cream.........

As I mentioned earlier, polynomials are often found in equations involving volume. So let be go through a problem that involves adding, subtracting, and multiplying polynomials.

So suppose we have an ice cream cone. How much ice cream is in it. You can figure this out by splitting the ice cream cone into the cap (which is a half a sphere) and the cone.

 * (volume of ice cream) = ? * (sphere) + (cone)

now figure this out you need to add two polynominal expressions and you end up with something like where r is the radius of the cone and h is the height of the cone. But I'm hungry, I want a double scoop.

 * (volume of ice cream) = ? * (sphere) + (sphere) + (cone)

Or since I don't know how many scoops of ice cream I want. I just have n scoops.

 * (volume of ice cream) = (n ? ?) * (sphere) + (cone)

So we can figure out the volume of ice cream. Well since there are a lot of business people out there, lets think about costs. Let p be the cost of ice cream per cubic centimeter. So we have

 * (cost of ice cream) = (price per volume) * (volume)

But we've forgotten something. We have the price of the ice cream, but what about the price of the cone......

 * (price of ice cream cone) = (price of ice cream) + (price of cone)

Now the price of the cone is going to be

 * (price of cone) = (price per area) * (area of cone)

We have get more complicated. We can take into account inflation and so make p and q variables which change year to year. Or we could try to figure out what fraction of the price of the ice cream cone is cone.

 * (fraction of price of cone) = (price of cone) / ((price of cone) + (price of ice cream))

Now I have actually put in algebraic equations for any of these things, because you haven't read chapter 5 yet, and I wanted to show you what the point of chapter 5 was before actually going through the content. But once you know how to add, subtract, multiply, and divide polynomials, you should be able to start with the equations for the volume of a sphere and cone, and the area of a cone and work to the end and get the (fraction of the price of cone) in an algebraic equation. I've worked through the equation in an appendix which you should read after you've gotten half way through chapter 5.

Now as far how do approach chapter 5. Think of the ability to add, subtract, multiple, and divide polynomials as a skill, like riding a bicycle. The best way of learning how to do it is to just keep practicing until its second nature. Something that I find useful is to make up problems and start with really easy problems, and then make them progressively harder. For example, an easy problem with adding polynomials is
 * 2x + x

which is of course
 * 3x

You can then make it a bit harder
 * (x+y) + 2x

which is
 * 3x + y

and just work your way up until you can deal with longer and longer polynomials without your mind going numb (and given a large enough polynomial, your mind will go numb).

Something that has always helped me is to just think of the equations as squiggles on a page, and the lesson as rules for turning one set of squiggles into another set of squiggles.

One of the more important things that you will learn in this chapter are the product and quotient rules for exponents. The way I think about them is that they turn multiplication and division into addition and subtraction. Section 9.1 starts with radicals which is a different way of writing things.

Now I've saved what I think is the most important section for the end of the lecture. Section 5.7 is about negative exponents and scientific notation, and I don't think that the author of the text quite realizes how important that section is. Let me give an example of how important section 5.7 is with a money example. A good salary for an experienced programmer is about $80,000 per year. A good salary for a CEO is about $2,000,000 per year. The revenue for the University of Phoenix is $300,000,000 per year. The revenue for a state government is $10,000,000,000 per year. The revenue for the federal government is about $2,000,000,000,000 per year. Now if you are like me, your mind started to go numb somewhere along the way, and all you were seeing by the end were big numbers with lots of zeros. Now lets write them in scientific notation.

 * (salary for programmer) = $8 x 10^4
 * (salary for CEO) = $2 x 10^ 6
 * (revenue for UOP) = $3 x 10^ 8
 * (state government budget) = $1 x 10^10
 * (federal budget) = $2 x 10^12

Now I'm hoping that you notice that the last set of numbers is just easier to think about. The federal budget rather than being a number with lots of zeros is now a number with 12 zeros as opposed to one's salary which has 4 zeroes.

With the exponent rule we can do some more magic. For example, what do you suppose is the average tax burden per person in the United States. We'll we look up the population of the United States which is 200,000,000 or in scientific notation 2x10^7.

 * (taxes per person) = (federal budget) / (people in the US)
 * (taxes per person) = $2x10^12 / 2x10^7

with the magic of the quotient rule, this equals

 * (taxes per person) = $2/2 times 10^(12-7)
 * (taxes per person) = $10^5.

Which means that on the average a person pays about $10,000 per year in taxes.

We can play some more games. For example suppose UoP spend 10% of its budget on IT, how many programmers is that......

 * (UoP IT budget) = 10% times $3 x 10^8
 * (UoP IT budget) = $3 x 10^7

Now each programmers salary is about $10^5, and
 * = $3 x 10^7 / $10^5
 * = 3 x 10^2

which says that UoP probably has around about 100 ? 500 people in IT. Notice that I did that with very little math. I've found this to be really useful in reading corporate reports. For example, if I know that a vacuum cleaner manufacturer made $10^6 a year last year, I can guess that each vaccuum cost between $10^2 and $10^3 and so they manufactured between 10^3 and 10^4 vacuums.

Rather than thinking in term of standard numbers and having my mind blank out from zeros, I rewrite the numbers in scientific notation, and then with the exponental and quotient rules can start making some quick calculations, like how many employees does the company have, what is its market capitalization, how does the size of this company compare with other companies, how many widgets did the company sell.

So rather than being called ¡°Negative Exponents and Scientific Notation¡± it should be called how ¡°You Can Handle Really Big and Really Small Numbers Without Going Crazy¡±

Hope that was useful.

Types of Polynomials
In one of the questions last week, I asked about what to do if you have a large polynomial. One of the important things to look at the polynomial and look at how big the largest exponent (or order) is. In MTH 208, you dealt with order-1 polynomials, which were linear equations. These involved straight lines. Since we are in MTH 209, we now learn how to deal with more complex polynomials, mainly those of order 2. Where you see those polynomials can be shown in the following chart.

Factoring
Now in order to solve these more complex equations, we need to take a short detour into factoring. Factoring is cool, and section 6.1 didn't explain how cool it is.

The reason factoring is cool is that multiplication is easy but factoring is hard. Multiplying two numbers together is like scrambling eggs, and factoring is like trying to unscramble eggs.

For example suppose I have two numbers say...
 * 3490529510847650949147849619903898133417764638493387843990820577

and
 * 32769132993266709549961988190834461413177642967992942539798288533

If I multiply them together, I get this one big number...
 * 114381625757888867669235779976146612010218296721242362562561842935706935245733897830597123563958705058989075147599290026879543541

Now the hard part comes if I give you this big number and then offer you money to figure out what two numbers I choose to get that big number. We can use the techniques we learned last week to figure out how long that will take. We want to factor a 110-digit number, and suppose we know that there are two factors. We then know that one of the numbers must be less than 55 digits. So we try all the numbers between 2 and 10**55.

Suppose we have a computer that can process a billion (10**9) numbers per second. So to look at all the numbers
 * 10 ** 55 numbers / 10 ** 9 numbers per second = 10 ** 46 seconds.

Now there are 3 x 10 ** 7 seconds per year. Now 3 is almost the square root of 10 so it is about 10 ** (1/2). So we can express this number as 10 ** (7.5).

So
 * 10 ** 46 seconds / 10 ** 7.5 seconds per year = 10 ** 39.5 years

Which poses a small problem since there has been 10 ** 10 years since the big bang. So factoring this number brute force will take 10 ** 29 times the lifetime of the universe. Note that getting a faster computer won't help you very much. If your computer is a million times faster, the time it will take to solve this problem is only 10 ** 23 times the lifetime of the universe. Now you can get somewhere if you find some mathematical shortcuts that identify possible factors, and that how they managed to factor that number, but without a basic breakthrough in mathematics, you can overwhelm those shortcuts by choosing an even bigger number to factor.

But there is actually a use for this, and you use it every time you buy something from ebay or send your credit card number over the internet. I can create a mathematical lock box and write a big number on it. Only the person who has a factor of that number can open the box, and the cool part is that you can create that big number without knowing the factor. This is what your web browser does when it sends a credit card number. It creates a big number that only Ebay or Microsoft or someone else knows how to factor, and mixes that number with your credit card number.

Needless to say, there is some very big money involved in being able to factor big numbers. To give you some idea how big, take a look at rsasecurity.

The reason it useful to factor polynomials is that it lets you solve polynomial equations. Suppose you have an equation
 * x ** 2 + (something) * x + (something else) = 0

if you can figure out a way of rewriting it so that it looks like
 * (x - a) (x - b) = 0

Then you know that a and b are solutions of the equation. One thing about polynomials is that if the highest term in the polynomial is x ** n, you should be able to split it into n factors, which means that there are n solutions to the equation. You can sort of see how this works by going the other way.
 * (x - a)(x - b)(x - c)

is going to end up with a polynomial with x ** 3 in front.
 * (x - a)(x - b)(x - c)(x - d)

is going to end up with a polynomial with x ** 4 in front and so forth.

Where this would be useful is if you have a business problem with an x**2 in it. Typically this be the case when you have a problem that involves area. One example of this would be a situation where you are running a pizza parlor. The price of a pizza is typically a quadratic equation
 * ($1.00 per square foot of dough) * (area of pizza) = (cost of pizza)
 * $1.00 * pi * r ** 2 = (cost)
 * $3.00 * r ** 2 = (cost)

So how big does the pizza need to be to cost $12.00?

 * $3.00 * r ** 2 = $12.00
 * r ** 2 = $4.00
 * r**2 - $4.00 = 0
 * (r + $2) (r - $2) = 0 (Where did this come from?)

 * r = $2 or -$2

Note that you end up with an extra root. This is because you are dealing with a second degree polynomial and so the solutions to it will usually have two answers.

The good news is that if you can factor a polynomial you can solve it. The bad news is that as we have seen above factoring is sometimes hard. Now scrambling an egg is straightforward. Unscrambling it is much harder. Chapter 6 has some techniques for unscrambling a two egg polynomial omelet. Once you put another egg in there, it gets much harder.

Incidentally in terms of general usefulness, the formulas for squaring (a+b) and for reducing a**2 - b**2 are worth remembering. Somehow they manage to turn up in all sorts of places. Actually solving a quadratic equation by factoring is something that is much less useful. The problem is if someone hands you a quadratic equation in the real world, the odds that it will separate cleanly into nice numbers is small.

In chapter 7, we are looking at rational expressions, which is another fancy way of saying fractions with polynomials. The first section is on simplifying rational expressions. The result for this is that suppose you have a fraction 1/4 and someone else has a fraction 2/8. They are actually the same thing, and so it's nice to put all of them into one common format. Then there is more stuff with multiplying, adding, and subtracting polynomials (i.e. slicing and dicing numbers).

I don't know why I have some many food metaphors this week. Maybe I can order online for some pizza and have Domino's factor some of my numbers.

Introduction
This week's assignment there are three threads in this weeks assignment which all build on the work we did last week. In the last week, you learned to work with rational expressions. This week's work uses those rational expressions to solve word problems involving rates. Also in last week's lesson you learned to solve equations using factoring. This week we will learn another way to solve quadratic equations using a single formula. Finally, we are going to learn out to solve power equations.

Rational Expression Word Problems
There are two parts of solving a problem. The first is writing the problem down as a equation, the second is solving the equation. Generally the first part of the problem is the hardest part. One you have an equation, solving it is usually easy using the techniques we've learned in the previous weeks. The hard part is setting up the problem. So I'd like into a bit more detail about how that works. Also, I'd like to use as an example, a problem that is more relevant to business than the standard algebra textbook problem.

So let me work through a problem.The V Corporation is a dot-com with huge problems. It has $40 million in the bank and it spending it at a rate of $8 million per month. The venture capitalist is willing to fund $15 million if it can prove that the V Corporation will be around in two years.

The question that faces the executives of the V Corporation how much do they have to cut their burn rate in order to survive two years when hopefully the economy will improve.

The first thing to do is to just write down, what you know and what you want to find out.

I know
 * $40 million in the bank now
 * $65 million if VC funding goes through
 * $8 million burn rat
 * goal is 24 month survival

I want to find
 * How much do I want to cut? Call this x

The next thing to do is to draw a chart

Since Burn = Time * Money
 * 65 = (8-x) * 24

I'll let you grind through the numbers and break the bad news to the employees of the V Corporation.

Note that this is just a simple linear question, not a fancy rational one. Let try something more complex.

I have two plants that are produces 40 cars per month. I know that one of the plants is producing 1 car every two days, and I want to see how this will impact production if I half the amount of time it takes to produce a car at the other plant.

I know
 * total production 30 cars per month
 * production at Plant #1 is 2 cars per day

I want to find out
 * how long it takes to build a car at Plant #2 (?)

So I draw my chart

Since we know that cars = rate * times, we can fill out some more stuff

We then can add together the number of cars we have each month to get the equation
 * 15 + 30 / x = 40

Multiplying each side by x we get
 * 15 x + 30 = 40
 * 15 x = 25
 * x = 25 / 15
 * = 5 / 3

So it takes a little more than a day to create a car at plant 2

We can then play some what if games. Suppose we double production at plant #2

Filling in stuff in we get

We can play some more games
 * What happens if we add a third plant that produces a car every two days?
 * We want to increase production to 100 cars a month and have two choices, we can increase production at plant one or build a new plant? How much do we need to increase production at plant #1 to build 100 cars per month, plant #2, what about building a third plant?
 * Alternatively the economy is bad, and there is now demand for only 30 cars a month. We can either leave plant #1 idle for part of the month or leave plant #2 idle for part of the month?  How much do you have to idle plant #1 and how much to you have to idle plant #2?
 * Union rules say that you have to idle plant #1 and plant #2 the same  amount.  How many days do you have to idle both plants to cut production?

As an exercise you can try to go through each of the above scenarios and see if you can handle it. If you don't run an auto company, you can try replacing cars and plants with something in your own experience.

One final thing. You notice that I've put everything in nice neat rows. Mathematicians don't do problems that way, but you see these sorts of tables everywhere in business. Part of the reason to put these sorts of problems in table format is that it helps you to also put those sorts of tables in Excel. For example, with the above scenarios is something that you probably would use Excel to help you with.

The Quadratic Equation
And now for for the second of the three threads in this weeks lesson.

You've seen three ways of solving quadratic equations
 * factoring
 * completing the square
 * the quadratic equation

One thing that will be useful for you do to know is that under normal circumstances, the quadratic equation is the only one that you will ever use. Factoring only works if you happen to have a problem that can be factored and those tend to occur only in math textbooks :-). Completing the square will work for everything, but you won't remember how to do it. The quadratic equation, is easy to use because you just put the numbers in the formula and out pops the answer.  It's short enough to memorize and even if you don't memorize it, its something that you can know exists and look up if you ever need it.

One thing that helps a lot in dealing with quadratic equations is to visualize what a quadratic function looks like.

The equation
 * a x**2 + b x + c

is going to be a U shaped parabola if a is positive and an upside down parabola if a is negative. Changing a changes how narrow the parabola is. Changing b moves it left and right and changing c moves it up and down. If you imagine an intersection between a U and a straight line, you can see that some of the time, you get two intersections, some of the time, you get one intersection, and some of the time you get no intersections.

One equation you might have at this point is the quadratic equation is the most useful way to deal with quadratic equations, then why did we spend most of last week talking about them.

The reason that mathematicians are interested in factoring has to do mainly with higher order equations. There are formulas for the cubic and quartic equations, but they take up two pages and no one ever uses them. What gets even more interesting are quintic and higher equations. A person named Galois proved in the early 19th century that there are *no* general formulas for 5th degree and higher polynomials. He was 21 at the time, and shortly (i.e. days) after proving this and inventing an entire branch of mathematicians, he lost a pistol duel over a woman of questionable morals. And his great legacy to the world was leaving the world the knowledge that solving the equation
 * <span style="color: rgb(204, 0, 0);">0 = a + b x + c x ** 2 + d x ** 3 + ... + x ** n

is really, really hard when n is larger or equal to five. But there is good news, which comes in the section on power equations ....

Power equations
The bad news is that general polynomials are hard to solve. The good news you usually won't see a general polynomial often and that a lot of the time you will see a subset that is much easier to solve. If you see the equation
 * <span style="color: rgb(204, 0, 0);">x ** n = b

You can solve it by taking the n-th root of both sides, giving you
 * <span style="color: rgb(204, 0, 0);">x = b ** (1/n)

There is a subtlity though. If you multiply a number by itself, the negative signs disappear. So the solution to
 * <span style="color: rgb(204, 0, 0);">x ** 2 = 4

is both 2 and -2. By contrast,
 * <span style="color: rgb(204, 0, 0);">2 ** 3 = 8

but
 * <span style="color: rgb(204, 0, 0);">(-2) ** 3 = -8.

The consequence to this is that there are two solutions to a power equation if n is even and b is positive, and no real solutions if n is even and b is negative. By contrast if n is odd, then you have one solution regardless of whether b is positive or negative.

Conclusion
If the three threads in this weeks lesson look unconnected, its because they are. At this point, you've mastered the basics of manipulating equations, and what is left now is to teaching you mathematical tools which you can use to solve different classes of equations. These tools are specialized, which means what works with one type of equation will completely fail for another type, but the more tools you have in your toolbox, the more likely it is that something will fit the equation you are trying to solve.

Lecture 4
My how time flies. We have one more week of new material and then a final week of review. This week there are three new concepts, the first is graphing quadratic equations, the second is doing quadratic inequalities, and the third is doing rational inequalities.

Graphing Quadratic Functions
The first new concept is graphing quadratic functions. I've generally found graphing functions to be useful because it gives you some visual idea of how that function behaves. So lets start with the quadratic equation
 * y = a x ** 2 + b x + c

There are examples of what you get if you graph that equation in section 10.3. The thing that these graphs, particularly figure 10.4, should remind you of is a ball flying through the air. This is not a coincidence as the equation that describes a ball flying through air is a quadratic equation. Now if you were to draw a picture of a ball flying through the air, you could do this if someone gave you three points: So lets try to figure out where the ball hits the ground. The equation that describes where the ball hits the ground is
 * where the ball starts from the ground.,
 * the highest point of the ball, and
 * where the ball hits the ground again
 * 0 = a x ** 2 + b x + c

and you can find these points via the quadratic equation or by factor. Notice that there are usually two such points. Now the highest point of the curve is midway between the points that the curve hits the ground. And that is at
 * x = -b / a

You can find the y value of the equation at that point by substituting back into the quadratic equation. This gives you three points, where the ball leaves the ground, where the ball is at its highest point, and where the ball hits the ground again. You can then connect the dots and draw a quadratic equation.

And now for the usual question. Why would you want to do this?

During last weeks discussion, we talked about a situation where a vendor would want to give a discount on their software depending on how many licenses one buys. Suppose the base price for a license is 200, but the vendor is willing to discount $5 for each license. The equation that describes the total cost is
 * y = x * (200 - 5x)
 * = -5 x **2 + 200 * x

Now one might want to know how the cost of the software varies with the number of licenses, and this is a good example of where graphing this on a sheet of graph paper might be useful. I'll leave this as an exercise for you, and once you graph it, you should realize that this is probably not a good deal for the vendor if you want to buy a really large number of licenses.

Quadratic Inequalities
This leads to the next topic. You are a purchaser and you will consider the deal only when the total cost is less that $1000. This creates an equation
 * 1000 < x * (200 - 5x)

or
 * 0 < -5 x ** 2 + 200 * x - 1000

There are two ways of solving this equation. If you can factor the equation, then you can find the signs of the factors. If they are the same, then the equation is greater than zero. If they are different, then the equation is less then zero. You can draw things on a number line similar to 10.15, and figure out where your equation is satisfied. The other way is to find the zero-crossings using the quadratic equation, you then pick a test point between the zero-crossings, and some test points outside the zero-crossings. This will tell you the sign of the equation, and you can see where your inequality is satisfied.

Rational Inequalities
The final topic for this week involves rational inequalities. An example where this would be the case is if you had a situation in which the total cost producing an item is $250 plus $5 per item. The unit cost of the item would be
 * <span style="color: rgb(255, 0, 0);">250 + 5 x
 * <span style="color: rgb(255, 0, 0);">--
 * <span style="color: rgb(255, 0, 0);">     x

You want to know howmany items you need to produce so that the cost of each item is less than $10.
 * <span style="color: rgb(255, 0, 0);">250 + 5 x
 * <span style="color: rgb(255, 0, 0);">--   < 10
 * <span style="color: rgb(255, 0, 0);">      x

The rule for doing rational inequalities is that you shouldn't multiply factors on both sides of the inequality, just add and subtract them. This gives you
 * <span style="color: rgb(255, 0, 0);">250 + 5x
 * <span style="color: rgb(255, 0, 0);">-- - 10 < 0
 * <span style="color: rgb(255, 0, 0);">     x
 * <span style="color: rgb(255, 0, 0);">250 + 5x       10x
 * <span style="color: rgb(255, 0, 0);">-- -  -- < 0

<div style="color: rgb(255, 0, 0);">
 * x                 x
 * 250 - 5x
 * -- < 0
 * x

The numerator is positive if x < 50 and negative if x > 50. The denominator is negative if x <0 and positive if x > 0. Thus the signs are different if x < 0, the same if 0 < x < 50, and different if x > 50. Thus the inequality is satisfied if x > 50.

Conclusion
I mentioned last week that you can think of algebra as a set of mathematical tools in your toolbox. This week we've added three more tools in your toolbox. That's all of the tools for this class. Once you get past this week, the next thing to do is to review all of what we have covered.

title: Talk:Algebra/ToInclude


text:
User talk:Albertde

Right now, my preoccupation is about learning languages from a Native English speaker's point of view. What does that mean? If you want to learn another Indo-European language, you need to understand how English differs from other languages in that family and what some common English idioms are. In particular:

 * 1) The | Great Vowel Sound Shift, which led to a massive change in pronunciation,
 * 2) The common every day words in English come from the Germanic core because Old English was a language similar to German.
 * 3) The invasion of England by the Vikings, who shared many words but had a different grammar led to the erosion of grammatical endings like two pieces of sandpaper rubbing against each other. Words like skin, die and they come from the Vikings.
 * 4) English got a new layer of vocabulary from Norman French after the conquest of England in 1066 by William the Conqueror. Some of the words in this layer were then later disguised to make certain words look like they had been derived directly from Latin. So parfait was transformed into perfect, originally with a silent c and det became debt, with a still silent b.
 * 5) English has in more recent times indulged in massive borrowing of words from Latin and then Greek.

Some English idioms include: Albertde 20:28, 17 June 2006 (UTC)
 * I am hungry.

Hi Albertde

Sorry for not answering on Talk:Dutch/Lesson 11. I haven't been here for a while. I do not agree with what you are saying about Dutch word order. To me the two versions:

 * ik dacht dat hij komen zou
 * ik dacht dat hij zou komen

are about evenly acceptable.

There may be some regional differences. The South probably more the latter (I'm from around Dordrecht).

152.1.193.137 21:43, 22 March 2007 (UTC)

Hi Albert

I have written a new chapter Dutch/Lesson 18 to address the @#$# word order problem. I have tried to cut it up in many little bits and pieces because for Anglophones it is really a big problem. If your mother tongue is German you start from the tenth floor up rather than from the basement and a lot of differences in details immediately strike you. (I have the same with German) Also: I really have to think how exactly we do these things... I do them automatically of course. ciao Iarlagab 21:57, 14 May 2007 (UTC)

P.S. As far as north-south bias is concerned: I try to stay away from that as much as I can, because I think we speak one language within which a certain variability is an asset not a curse. Besides, who am I to decide what version of Dutch is better? Or impose that on others? But of course, I am a northerner and would need southern input to correct bias.

title: User talk:Albertde


text:
Talk:General Astronomy/Observational Astronomy

These are lecture notes I wrote for a course at the University of Phoenix. They are released to wikimedia under an appropriate creative commons license.

Roadrunner 20:58, 17 June 2006 (UTC) One problem with astronomy textbooks is that they don't mention how messy things really are. Everything is packaged in nice neat packets of information, and not much effort is spent describing the amount of effort it takes to get some real data. There is a lot of unglamourous grunt work that is involved in doing experiments, and that needs to be mentioned because most of astronomy doesn't consist of eureka moments, but rather a large amount of it consists of things that are tedious staring in front of a computer screen doing data reduction.

Getting data always starts with the instrument, and that usually means a telescope of some sort. You can think of a telescope as just a giant light bucket which is catching light particles from the sky and focusing them into a detector at the end of the telescope.

In ancient times (i.e. before 1980), what would be at the end of the telescope would be likely be a camera. The camera wouldn't use film but instead would record everything on a glass plate. Glass plates were needed instead of plastic because they stored better and didn't expand or contract as much over time.

Today, we are in a transition period between film cameras and digital cameras. However that transition happened in astronomy in the 1980's and many of the reasons that astronomers started using digital cameras are the same as the ones people are moving from film to digital cameras. The big one is that you can download the image onto your computer and then have the computer do image processing. This also means that you can store pictures, transmit them over the internet, and copy them to your friends. You can also instantly look at the picture and know if you took a picture of the right thing or if you need to reshoot the picture rather than waiting for the pictures to come back from the dark room. Finally, one other thing that is very important to astronomy is that digital cameras are far more sensitive to light than film cameras are. A film camera will catch about 5% of the light hitting it, while a CCD digital camera typically catches about 95% of the light which hits it. This isn't immediately obvious with a digital camera, but one thing that you can try if you have a digital camera is to take a picture at night, and you'll find out that it comes out much better than a film camera.

So when digital cameras first came out, plate photographs very quickly became obsolete, and most older observatories today have dark rooms and storage rooms for photochemicals, and these rooms are largely empty.

The digital chips which are at the end of most telescopes are largely the same as the ones in consumer digital cameras. There is one big difference in that the ones at the end of telescopes are generally cooled by liquid nitrogen. The reason for this is that a digital camera will pick up some noise from heat, and you want to reduce that noise as much as possible.

So you have a digital camera at the end of an instrument at the end of a telescope. Typically, in an observing run, you wake up at about 3 p.m. During the day the technicians will have installed the instruments that you need for a nights observing run. You go to the telescope at 3 p.m., check to see that everything is installed correctly, since you don't want to wake someone up at 3 a.m. if something breaks. You then spend the next two hours before sunset taking some calibration shots. One image set that you take involves closing the shutter, and taking an image of black. Even though the CCD chip is soaking in liquid nitrogen, there is still some noise in the picture that you want to get rid of. Another set of images you take, involves pointing the telescope at a spot on the wall which has been painted white. The reason for the white picture is that the different parts of the CCD chip will have different sensitivities. There are also cracks and dust and other noise on the CCD that you want to subtract from your observations. About this time, its dinner (or breakfast), so you head off and eat and come back when the sun starts setting.

After the sun starts setting, your first goal is to find the object that you are trying to photograph. You can punch in the coordinates into the computer, but that will only point the telescope in the general area of the sky that you are interested in. The next thing that you have to do is to take out your star atlas, and look for a pattern of stars that is close to the thing that you are looking for. This is a lot like driving in an strange city when you are looking at the monitor and then trying to match the patterns you see with the patterns on the chart.

So you've now found the object you are looking for. The next step is what has been called the world's slowest video game. The problem is that you want to keep the shutter open for a long time (say thirty minutes) to capture as much light from the object as possible. The trouble is that in that time, the sky moves. The telescope is trying to track the object, but the tracking isn't perfect. So you have to make adjustments to the telescope. What that involves is to mark the location of some stars on the television monitor with a grease pencil, and then if the stars start to drift, you use the control panel to move the stars back. The annoying thing is that you have to keep your eyes on the monitor. In between these measurements, you take some snapshots of a calibration device. If you are looking at spectra, you take picture of a flourscent lamp that has lines in certain known positions. If you are measuring brightness, then you need to take some pictures of a star whose brightness is known.

So after a night of all of this, you now have some data on hard disk, and you go to sleep. The next few weeks is where the hard part comes in. You see you have a lot of raw data, but it's not very useful to anyone. The problem is that none of the data has been calibrated. So you spend the next few weeks taking the data, subtracting the black leve, correcting the white levels, stretching and shrinking the picture so that you know what the frequencies of your spectra are. You might also be spending your time doing things like trying to correct for the effects of dust in the galaxy. Through it all, you are probably using an astronomy package called IRAF, which you like all big software packages has its cute bugs and idiosyncrasies.

After all of this, you now have tables and charts which the world is interested in. You then type up a paper, and then upload it to www.archvix.org and then send it off to a journal. The journal then takes the paper submits it to three anonymous referees who then evaluate the paper. In some cases, they will give the go ahead to publish. In very rare cases, they will say that the paper is beyond hope of publication. In most cases, they will return the paper with

After all of this, you now have tables and charts which the world is interested in. You then type up a paper, and then upload it to www.archvix.org and then send it off to a journal. The journal then takes the paper submits it to three anonymous referees who then evaluate the paper. In some cases, they will give the go ahead to publish. In very rare cases, they will say that the paper is beyond hope of publication. In most cases, they will return the paper with some comments, questions, and suggestions, and there is usually some back and forth before the paper is approved.

In the mean time, you are busy thinking up of experiments and observations you want to do next, and are spending your time reading up on what the latest data is, helping to design new instruments for your telescope, or working on proposals to get telescope time or grant money.

It's a very long slow process, and its full more of hard work than of eureka moments. But as things plod along, you get more and more data, and slowly it becomes more and more clear what is going on out there in the universe.

Polaris location
The text states that Polaris is on the "cup" of the Big Dipper (Ursa Major). This is incorrect- Polaris is at the end of the "handle" of the Little Dipper (Ursa Minor). May I correct this or can someone else do it please? That glaring mistake says a lot about the accuracy of the rest of the text. Perhaps the author meant to say that the cup of Ursa Major points to Polaris? That's how I learned to find it as a child, was by following a line from the cup of the big dipper.
 * Yes, you may correct it. That is the point of a Wiki. If you like, you can add a diagram as well. There are lots of images to choose from at Wikimedia Commons.  --Jomegat (discuss • contribs) 00:33, 1 December 2012 (UTC)

Aesthetic Bold - mid sentence
I was going through each chapter and removing the bold terms that are part of a sentence especially mid or end. However this is more to do with aesthetic use of bold and flow so maybe the original author would like the terms in bold left in.

Opinions welcome

--Sluffs (discuss • contribs) 23:31, 14 August 2015 (UTC)


text:
User:Rdelre

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally. --Think Fast 21:00, 17 June 2006 (UTC)

title: User:Rdelre


text:
General Astronomy/Current Unsolved Mysteries

Dark Matter and Dark Energy
Dark matter is invisible, but has been postulated from its apparent influence on visible matter. It is one explanation for the observed strength of gravity needed to hold galaxies and clusters of galaxies together. Without considerably more mass than can be detected with telescopes, roughly 10 times more, these systems should simply fly apart. The dark matter theory hypothesizes that matter exists that emits little or no radiation and therefore is not observable with telescopes. Dark matter might also be needed to explain the cosmic microwave background (CMB) power spectrum. Some proposals for explaining dark matter are, for example, particles like weakly interacting massive particles (hypothetical WIMPs) or neutrinos, or massive compact halo objects (MACHOS), or ordinary matter that is hidden somehow, or modified gravity (MOND, MOG, f(R)), or some combination of these things.

Another hypothesis, dark energy, has been proposed to explain the surprising observation that the expansion of the universe is getting faster. This acceleration of the expansion was discovered by measuring a certain type of supernova, called type Ia, in surveys of galaxies. Type Ia supernova are used since they all have the same absolute brightness. (We will discuss why they have the same absolute brightness, and how they are used to measure distances, in a later chapter, General Astronomy/The Death of High Mass Stars). This makes them very useful for measuring distances. It had been anticipated, before the measurements were made, that the expansion of the universe would be decelerating, due to the gravity of all the matter. Dark energy is postulated to explain the apparent repulsive force pushing things apart. Ongoing research efforts are to measure the expansion rate more accurately, and discover the nature of dark energy.

Dark matter is generally accepted to exist, though questions remain. It is probably not regular matter made of protons and neutrons (baryonic matter). That is because a higher density of ordinary matter during the nuclear reactions occurring in the first few minutes of the universe (known as big bang nucleosynthesis), would be expected to produce different abundances of light elements and their isotopes, like deuterium, than are actually observed. Another problem for ordinary matter is that the "clumpiness" of the observed galaxies and the cosmic background radiation is not what would be expected from predictions. Other considerations tend to disfavor neutrinos as dark matter as well.

Alternatives to the dark matter hypothesis are new forces or modified gravity theories. There is speculation that there is another large-scale force that is keeping our universe together. Another possible explanation is to think of space as a gas-and-space solid. If you place two objects apart from each other then pressurize the area, the two objects will be forced towards each other. This reverses our current ideas of gravity from an object having a pull on other object, to an object being pushed from all directions. (An object alone has no movement, but two objects create an uneven pressure pushing the objects together.)

An estimated 23% of the matter in the universe is dark matter. Ordinary matter only makes up 4% of the universe. The remaining 73% is an even more mysterious, repulsive "dark vacuum energy".

The most popular theory right now is that the repulsive force is actually a property of space itself: it is caused by waves of energy, created by particles and anti-particles popping into existence and then annihilating each other with no net effect. Early in the universe, when there was not much space, the effect was small compared to gravity. But as the galaxies moved apart, the effect became greater.

History and Ideas of Composition

Dark matter was first proposed in 1933 by Swiss astrophysicist Fritz Zwicky to explain the orbital motions of galaxies in clusters. He observed that there was apparently much more mass in a cluster of galaxies than just the visible objects, like stars, gas, and dust. So there was something unseen adding to the mass of the cluster. Later, when X-ray telescopes became operational, they revealed a cloud of hot hydrogen gas between the galaxies, accounting for part of the missing mass. Beginning in the 1960's, Vera Rubin discovered that contrary to Kepler's law that objects orbiting around a central body move slower the farther away they are, that in fact the orbital speed of stars in galaxies remains roughly the same beyond a certain distance from the galaxy core. So there has to be some extra matter, either in the flat disk of galaxies or in a spherical halo around the galactic core. Building on Zwicky’s work she concluded that this extra mass was dark matter. The term dark matter refers to matter that is perceived to be present because of its effect on the objects around it. While the composition of dark matter is still unknown, scientist have proposed some possible candidates that dark matter could be. They are:

 * Ionized gas — Emits thermal free radiation which cannot be observed.
 * Dust — Emits radiation and is made up of elements heavier that helium.
 * Main Sequence Stars — Could be an ingredient, but could not be sole component of dark matter because a great portion of them would be visible.
 * Black Holes — Are highly unlikely because they would disrupt the binary separations of dark matter. However, not much is known about the explosions that produce black holes, so it is still an option.
 * White Dwarfs — When forming, white dwarfs produce many intermediate-mass elements (He, N, Ne, C, O) or halo gas, which is not visible.
 * Neutrinos — Unlikely, but they do have enough mass to be a candidate.
 * WIMPS or Cold Dark Matter — Weak interacting particles, though they do move at nonrelativistic speeds.

A more in-depth flow chart depicting how the above suggestions are connected is picture below taken from Modern Cosmological Observations And Problems (140). http://ned.ipac.caltech.edu/level5/Bothun2/Figures/dm1.gif

Reionization
The cosmic background radiation was formed when protons and electrons combined to form atoms. The trouble is that we know that the matter between galaxies today is ionized (i.e. it's separate protons and electrons) with clumps of hydrogen atoms. We know this because when we look at all but the most distant galaxies, we don't see the spectra lines of hydrogen. So at some point the hydrogen in the universe reionized. The notion was that starlight caused the hydrogen in the universe to reionize, but the latest observations seem to indicate that this reionization occurred before the first stars were there.

Galaxy Formation
The idea is that galaxies started from tiny fluctuations in density that formed after the big bang. By assuming that the universe consists mainly of cold dark matter, you can almost get the clumpiness that you see with the current galaxies. But there are still puzzles. There is an annoying lack of tiny galaxies, and the rotation curve that cold dark matter predicts, isn't quite the one that we see.

Before the Big Bang
Now to get really speculative, there have been some papers written recently that try to figure out what happened before the Big Bang. One of the strange ideas is that the universe is merely one plane in a multidimensional space, and that what happened was that two membranes in a multidimensional space collided causing a massive expansion in three of the dimensions. This is all really speculative, but the weird thing is that it isn't totally disconnected from observation. The idea is that you can use this model to predict the initial expansion of the universe, and this might have some effects on the ripples that you see in the cosmic microwave background. The big problem is that the matter that began expanding had to have always existed, yet, because of the predictable nature of the elements, it had to have had a definite, external force to set it in motion that could decide when to start the "chain reaction". Something cannot just be in a stable form, or even an unstable form, forever and finally explode, it has to go in a cycle. In other words, consider the following. Out of nothing, a theretofore nonexistent dense mass spontaneously emerged, which erupted in an enormously powerful fireball by its own theretofore nonexistent energy to spontaneously and immediately create from this chaos the defined fundamental forces of physics and the subatomic fundamental particles, which eventually organized themselves into a variety of atomic species, then into molecules, and then into a diverse assortment of inorganic matter that gravitationally assembled itself into this highly structured and precisely ordered universe. We all know that this is ridiculous, but it is equally ridiculous to say "a theretofore stable mass spontaneously became unstable".

With all of these puzzles, its not clear what is going to happen next. There is a lot of data coming in, and it may be that with new data, it will be possible to make our models of the universe work with minor tweaks here and there, and we can go on in the mode of what Kuhn calls "normal science." It's also possible that one day there will be some observation which is like Galileo seeing the phases of Venus — some observation that makes absolutely no sense in the current paradigm of things, and this will force people to fundamentally change how they view the universe.

Discussion Questions
1) Find an old astronomy textbook, and compare it with a very recent one. What mysteries in the old astronomy textbook are now believed to be resolved, and what facts and statements in the old astronomy textbook are now believed to be incorrect?


text:
Talk:General Astronomy/Current Unsolved Mysteries

This is original material by Roadrunner for a course on astronomy for the University of Phoenix and released to wikimedia under the appropriate commons licenses

Roadrunner 21:17, 17 June 2006 (UTC)


text:
General Astronomy/The Drake Equation

The subject of extraterrestrial intelligence is one which has a fascinating mix of fact and speculation. In dealing with extraterrestrial intelligence there is one important fact which was first pointed out by Enrico Fermi, the scientist that built the first nuclear reactor, and it's an obvious fact that is so obvious that one doesn't realize how remarkable it is until one thinks about it. This is the fact that when one looks at the skies, there is no obvious sign of extraterrestrial life.

Where are they?
It's a remarkable fact, because even with our limited technology level, we've made the sun look very strange to an alien astronomer. Type G stars simply do not emit much radio radiation, and to any astronomer within a fifty light year radius of the earth, there is something blindingly weird about the sun, in that something is causing the sun to appear to emit vast amounts of radio waves. Once the sun has been identified as odd, it wouldn't take that much effort to start looking into the characteristics of the radio waves and through things like Doppler shift, quickly figure out that the radio waves didn't come from the sun but rather from a planet in orbit. Once that gets figured out, you can look at the details of the radio spectrum and piece together things like the rotation rate of the Earth (the amount of radio waves you will see will be sharply reduced when the Atlantic and Pacfic ocean are facing you in comparison to the continents), and someone who is sufficiently clever might be able to figure out how to decode the radio output of the earth.

The paradox becomes even more odd if you think ahead a thousand or two thousand years. Keep in mind that a thousand or two thousand years is nothing astrophysically speaking. If you can imagine what we ought to be able to do, assuming that rates of technological growth don't slow down, there ought to be many things that would be astrophysically obvious. For example, the ultimate answer to the energy resources is to build a series of solar satellites that trap solar energy and beam it to the earth or any other planet in the solar system. If you trap enough solar energy, this will start to become obvious in the solar spectrum, in that if you plot many stars in the HR diagram then you will soon find that there is something very odd about some of the stars that don't fit on the main sequence at all. Another technology that might be astrophysically significant is that of nanotechnology and self-replicating machines. It shouldn't be too hard in the next thousand years to produce autonomous robots that can feed off asteroids and reproduce. Once you have these robots roaming the stars, exponential growth makes it very likely that you will run into one of them.

So there is something odd to be explained. The problem here is that we have enough facts to establish that there is a puzzle, but not nearly enough facts to figure out what the solution is. There are many ways of resolving the Fermi paradox, and given the lack of facts to constrain the solution, we are more in the realm of science fiction than of science at this point.

Some of the solutions are extremely depressing. One solution is simply that technological civilizations destroy themselves. There is no end to the number of ways we could destroy ourselves now, and it's also possible that advancing technology could allow for ways of self-destruction that we haven't thought about. For example, what would happen if nanotechnology made it possible for any human being to create their own atomic bomb or a deadly virus?

There are also sociological explanations that are rather depressing. We happen to live in a society that for the most part thinks that technology and curiosity are good things. However, even looking at examples in our own history, it's not clear that the way that we look at the world is the most natural or the most stable. There are the classics of dystopian fiction 1984 and Brave New World, and one would imagine that these worlds aren't that conducive to stellar colonization.

It may be possible that when and if we start exploring alien worlds, we'll find that at least in our part of the galaxy, that some previous civilization managed to extinguish, for whatever reason, all traces of life and then destroyed itself. But then again maybe not.

Before one gets too depressing, let me just point out one other obvious fact that is even more amazing when you think about it. We do know that somehow, someway, we've made it this far. We don't know how probable or improbable life and alien civilization is, but we do know that somehow someway, it happened at least once on the Earth. We don't know what is the resolution of the Fermi paradox, but what we do find remarkable is that first that we might someday figure this out, and that somehow, at least to some people, it really matters.

Plus the sun is 93,000,000 miles away from earth.

 * The Drake Equation
 * Takes into account:

 * 1) Number of stars in a galaxy. (N*)
 * 2) Fraction of stars with planets. (fp)
 * 3) Number of planets in a system that reside within the life-zone for that system. (nLZ)
 * 4) Fraction of suitable planets on which life actually begins. (fL)
 * 5) Fractions of lifeforms which evolve to intelligence. (FI)
 * 6) Fraction of star's life during which lifeform is communicative. (FS)

The last factor is the hardest to estimate, along with the number of communicative civilizations per galaxy (NC). The probabilities cover several orders of magnitude.

title: General Astronomy/The Drake Equation


text:
Talk:General Astronomy/The Drake Equation

This is material from a course I taught at the University of Phoenix. I am releasing the material under the appropriate licenses.

Roadrunner 21:20, 17 June 2006 (UTC)

Hey, I did appreciate the work so far but this page seems to be a bit xenophobic. It would be nice if you changed the Bin Laden examples a bit - specially in an open content place where people from all over the world are going to read that. Hope the book gets completed soon, except for a few grammar mistakes it's absolutely great material


text:
User:Naib~enwikibooks

On the web: http://www.markfickett.com/

title: User:Naib~enwikibooks


text: Category:Book:Cantonese

title: Category:Book:Cantonese


text:
Statistics/Distributions/Continuous

A continuous statistic is a random variable that does not have any points at which there is any distinct probability that the variable will be the corresponding number.

Cumulative Distribution Function
A continuous random variable, like a discrete random variable, has a cumulative distribution function. Like the one for a discrete random variable, it also increases towards 1. Depending on the random variable, it may reach one at a finite number, or it may not. The cdf is represented by a capital F.

Probability Distribution Function
Unlike a discrete random variable, a continuous random variable has a probability density function instead of a probability mass function. The difference is that the former must integrate to 1, while the latter must have a total value of 1. The two are very similar, otherwise. The pdf is represented by a lowercase f.

Special Values
Let R be the set of points of the distribution.

The expected value for a continuous variable X with probability density function f is defined as $$\int_{R} xf(x)dx$$.

More generally, the expected value of any continuously transformed variable g(X) with probability density function f is defined as $$\int_{R} g(x)f(x)dx$$.

The mean of a continuous or discrete distribution is defined as $$E[X]$$.

The variance of a continuous or discrete distribution is defined as $$E[(X-E[X]^2)]$$.

Expectations can also be derived by producing the Moment Generating Function for the distribution in question. This is done by finding the expected value $$E[\exp(tX)]$$. Once the Moment Generating Function has been created, each derivative of the function gives a different piece of information about the distribution function.

$$\frac{d E[\exp(tX)]}{dt}$$ = mean $$\frac{d^2 E[\exp(tX)]}{dt^2}$$ = variance $$\frac{d^3 E[\exp(tX)]}{dt^3}$$ = skewness $$\frac{d^4 E[\exp(tX)]}{dt^4}$$ = kurtosis

title: Statistics/Distributions/Continuous


text:
Category:Book:Spanish

da:Kategori:Spansk fr:Catégorie:Espagnol hr:Kategorija:Španjolski jezik pt:Categoria:Espanhol zh:Category:西班牙语

title: Category:Book:Spanish