text:
User talk:Egm6936.f10/Probability concepts

Put your questions here.

= discussion 2011.09.22 =

Question 5
Xiu 2010, p.16. In order to generate non-uniform random variables, the most straightforward approach is via the inversion of the distribution function, for example, we can directly obtain the exponential random variable by inverting the exponential distribution. Given the exponential distribution density function is

$$\displaystyle f_{X}(x)=ae^{-ax}, a> 0$$

It's easy to get the distribution function as

$$\displaystyle F_{X}(x)=\int_{0}^{x }f_{X}(y)dy=\int_{0}^{x }ae^{-ay}dy=1-e^{-ax}$$.

Hence we have the exponential random variable by inverting the distribution function as

$$\displaystyle F_{X}^{-1}(u)=-\frac{log(1-x)}{a}$$

But for most cases that $$\displaystyle F_{X}^{-1} $$ isn't available in explicit form, which we should use approximation instead, like the normal distribution.

My question is can you explain in details how can we use approximation method to generate those random variables?

= discussion on 2011.09.15 =

Question 2
By your definition of the $$\sigma\,\;$$-field, $$\mathcal F $$, it's the collection of all subsets on $$\Omega$$. But from Xiu 2010, p.10, the $$\sigma\,\;$$-field, $$\mathcal F $$, is defined as the collection of subsets on $$\Omega$$. So, which one is better?

Answer 2
Clearly the definition of a $$\sigma\,\;$$-field $$\mathcal F $$ that includes all subsets of $$\Omega$$ is a stronger statement than the definition that only includes a collection of subsets of $$\Omega$$. The definition that is weaker is more general, i.e., the one that only includes a collection of subsets in $$\Omega$$. We need to look up some references to verify, e.g., some mathematical statistics / probability books.

Consider a counter example to the statement that we only need a collection of subsets of $$\Omega$$ to form a sigma-field: $$\Omega = {1, 2, 3}$$ $$\mathcal F :={\emptyset, 1, 2, \Omega}$$ $${1}\cup {2}={1, 2} \notin \mathcal F$$ Clearly, $$\mathcal F$$ can't be a sigma-field. The point here is that you can't take any arbitrary collection of subsets of $$\Omega$$ to form a sigma-field, but you need to take a collection of subsets of $$\Omega$$ that satisfies 3 conditions for the set $$\mathcal F$$ to be a sigma-field.

Three conditions that the sigma-field must satisfy:

$$\bullet$$ Not empty:$$\Omega \in \mathcal F$$ and $$\emptyset \in \mathcal F$$;

$$\bullet$$ Given $$A \in \mathcal F$$, then $$A^c \in \mathcal F$$;

$$\bullet$$ Given $$A_1$$, $$A_2$$,...$$\in \mathcal F$$, then

$$\bigcup_{i=1}^{\infty} A_{i} \in \mathcal F$$ and $$\bigcap_{i=1}^{\infty} A_{i} \in \mathcal F$$.

Question 3
For continuous distribution, the probability of any particular value is zero, $$\displaystyle P(X=x)=0, \forall x \in \mathbb R$$. Mathematically, I can understand this concept, that's since the distribution is continuous, we have

$$\displaystyle \lim_{\epsilon \rightarrow 0}F_{X}(x+\epsilon )=F_{X}{(x)}, \forall x$$.

But intuitively, I can't fully accept it. Why the probability of any particular value is zero?

Answer 3
For discrete events, like throwing a dice with 6 facets, you can talk about the probability of having, say, number 3, and that's 1/6.

But for continuous events, you need to think in terms of the area under the curve, similar to using the trapezoidal rule to integrate.

A better explanation would be that there are infinitely many real numbers; the set of real numbers, unlike the set of integers, is very dense. For example, given any two numbers that are very close to each other by $$\displaystyle \epsilon$$, with $$\displaystyle \epsilon$$ being very small (as small as you can imagine, e.g., $$\displaystyle 10^{-36}$$), you can always find infinitely many real numbers in between these two numbers.

So for continous events described by real numbers, the probability of throwing a "generalized dice" to get a particular real number is zero !

Question 4
Xiu 2010, p.15 : In order to generate nonuniform random variables, the inversion of a distribution function, i.g.,Inverse transform sampling is the most straightforward method. Assume the cdf of $$\displaystyle X$$ is $$\displaystyle F_{X}(x) = P(X < x)$$(Note: In Xiu 2010, p.15, $$\displaystyle F_{X}(x) = P(X \leqslant x)$$ is used here). For strictly increasing and continuous $$\displaystyle F_{X}(x)$$, we can solve $$\displaystyle F_{X}(x) = u$$ to get the unique root as $$\displaystyle x = F_{X}^{-1}(u)$$, $$\displaystyle 0 < u < 1$$. For distributions with discontinuity, $$\displaystyle F_{X}$$ is not strictly increasing, and we need be more care to find its inverse. For the left-continuous version
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$$\displaystyle F_{X}^{-1}(u) := \text{inf} \{x\mid F_{X}(x) > u, 0 < u < 1 \}. $$ (2.7)
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Note:

In Xiu 2010, p.15, Xiu has used $$\displaystyle F_{X}^{-1}(u) := \text{inf} \{x\mid F_{X}(x) \geqslant u, 0 < u < 1 \}$$. Actually, this is the definition for the inverse of right continuous cdf.

Following Proposition can help justifying the inversion method for generating nonuniform random numbers.

Proposition 2.11:

Let $$\displaystyle F_{X}(x)=P(X < x)$$ be the cdf of $$X$$. Then we have following results.

$$\displaystyle \bullet$$ $$\displaystyle u\leqslant F_{X}(x)\Leftrightarrow F_{X}^{-1}(u)\leqslant x$$, i.e., $$\displaystyle F_{X}^{-1}$$ is non-decreasing.

$$\displaystyle \bullet$$ If $$\displaystyle U$$ is uniform in $$\displaystyle \left ( 0,1 \right )$$, then $$\displaystyle F_{X}^{-1}(U)$$ has distribution function $$\displaystyle F_{X}$$.

$$\displaystyle \bullet$$ If $$\displaystyle F_{X}$$ is continuous, then $$\displaystyle F_{X}(x)$$ is uniform in $$\displaystyle \left ( 0,1 \right )$$.

Can you explain above proposition?

Answer 4
Fig 4.1: Continuous uniform distribution (pdf), U(0,1) Fig 4.2: Continuous uniform distribution (cdf), U(0,1) Fig 4.3: Distribution Function and Its Inverse Fig 4.4: Left Continuous Distribution Function and Its Inverse

Install inkscape to plot the figures that I drew in the above [[media:Hailong.2011_09_15_10_31_23.pdf |Explanation]]. See Writing tools. Discussion:

Function (mathematics)
A function is a mapping from set $$\mathbf A $$ to set $$\mathbf B $$, and satisfies:

1. For every element a in $$\mathbf A $$, there is an element b in $$\mathbf B $$ such that $$\langle a, b\rangle$$ is in the mapping; 2. If $$\langle a, b\rangle$$ and $$\langle a, c\rangle$$ are in the mapping, then b = c.

One-to-One: A function $$\displaystyle f$$ is said to be one-to-one (injective), iif whenever $$\displaystyle f(x) = f(y),\,x = y$$. Onto: A function $$\displaystyle f$$ from a set $$\mathbf A $$ to a set $$\mathbf B $$ is said to be onto(surjective), iif for every element $$\displaystyle y$$ of $$\mathbf B $$ , there is an element $$\displaystyle x$$ in $$\mathbf A $$ such that $$\displaystyle f(x) = y $$,  that is,  $$\displaystyle f $$ is onto iif $$\displaystyle f( A ) = B $$. Wikipedia on Function, Other resources on Function.

Fig 4.5: Function

Continuity
Definition:

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$$\displaystyle \forall \epsilon > 0 $$, $$\displaystyle \exists \delta > 0 $$, such that $$\displaystyle \left | x - c \right | \leqslant \delta \Rightarrow \left | F(x) - F(c) \right | \leqslant \epsilon $$ (eq1)
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Where $$\displaystyle c $$ is within the domain of $$\displaystyle F$$.

One-sided continuity
Left Continuity at a Point

We say that $$\displaystyle F$$ is continuous from the left at $$\displaystyle \hat{x}$$ when the limit from the left of $$\displaystyle F \left({x}\right)$$ as $$\displaystyle x \to \hat{x}$$ exists and:

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$$\displaystyle \lim_{\underset{x \in A}{x \to \hat{x}^-}} F \left({x}\right) = F \left({\hat{x}}\right) $$ (eq2) Fig 4.6: Left continuity
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Right Continuity at a Point

We say that $$\displaystyle F$$ is continuous from the right at $$\displaystyle \hat{x}$$ when the limit from the right of $$\displaystyle F \left({x}\right)$$ as $$\displaystyle x \to \hat{x}$$ exists and:

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$$\displaystyle \lim_{\underset{x \in A}{x \to \hat{x}^+}} F \left({x}\right) = F \left({\hat{x}}\right) $$ (eq3) Fig 4.7: Right continuity
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Where $$\displaystyle A $$ is the domain of function $$\displaystyle F(x)$$.

Minimum Vs. Infimum, Maximum Vs. Supremum
Let's look at some examples first.

Examples:

$$\displaystyle \text{Inf}\, \{ x: x \in (-1, 1)\} = -1$$

$$\displaystyle \text{Sup}\, \{ x: x \in (-1, 1)\} = 1$$

$$\displaystyle \text{Min}\, \{ x: x \in (-1, 1)\} \text{non-exist}$$

$$\displaystyle \text{Max}\, \{ x: x \in (-1, 1)\} \text{non-exist}$$ $$\displaystyle \text{Inf}\, \{ x: x \in [-1, 1]\} = -1$$

$$\displaystyle \text{Sup}\, \{ x: x \in [-1, 1]\} = 1$$

$$\displaystyle \text{Min}\, \{ x: x \in [-1, 1]\} = -1$$

$$\displaystyle \text{Max}\, \{ x: x \in [-1, 1]\} = 1$$

Definition:

Infimum of $$\mathbf A $$ is the greatest real number that smaller than or equal to every number in $$\mathbf A$$. If such number is non-exist (because $$\mathbf A$$ is not bounded below), then we define $$\text{inf}( \mathbf A ) = -\infty$$. If $$\mathbf A$$ is empty set, we define $$\text{inf}( \mathbf A ) = \infty$$.

Supremum of $$\mathbf A $$ is the smallest real number that greater than or equal to every number in $$\mathbf A$$. If such number is non-exist (because $$\mathbf A$$ is not bounded above), then we define $$\text{inf}( \mathbf A ) = -\infty$$. If $$\mathbf A$$ is empty set, we define $$\text{inf}( \mathbf A ) = \infty$$.

Also see infimum and supremum for real numbers, Wikipedia on Infimum, Wikipedia on Supremum.

Case A:

Fig 4.8: Strictly increasing, continuous (Case A)

$$\displaystyle \text{min}\left \{ x\mid f(x) > \hat u \right \} := \underset{ x > \hat x}{\text{argmin}} (f(x) > \hat u)$$ doesn't exist. $$\displaystyle \hat x = \text{inf}\left \{ x\mid f(x) > \hat u \right \} := \underset{ x > \hat x}{\text{arginf}}( f(x) > \hat u)$$.

Case B:

Fig 4.9: Monotonically increasing, left continuous (Case B)

$$\displaystyle \text{min}\left \{ x\mid f(x) > \hat u \right \} := \underset{ x > \hat x}{\text{argmin}} (f(x) > \hat u)$$ doesn't exist. $$\displaystyle \hat x = \text{inf}\left \{ x\mid f(x) > \hat u \right \} := \underset{ x > \hat x}{\text{arginf}}( f(x) > \hat u)$$.

Case C:

Fig 4.10: Left continuous (Case C)

$$\displaystyle \text{min}\left \{ x\mid f(x) > \hat u \right \} := \underset{ x > \hat x}{\text{argmin}} (f(x) > \hat u)$$ doesn't exist, $$\displaystyle \hat x = \text{inf}\left \{ x\mid f(x) > \hat u \right \} := \underset{ x > \hat x}{\text{arginf}}( f(x) > \hat u)$$.

Properties
(increasing case)

Statement I:
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$$\displaystyle \forall a,\, b \in \Omega$$, if $$\displaystyle a \leqslant b $$,then $$\displaystyle F_{X}(a) \leqslant F_{X}(b) $$ (eq4) Where $$\displaystyle \Omega$$ is the increasing domain of function $$\displaystyle F_{X}(x)$$.
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Proof Fig 4.11: Increasing monotonicity "Strictly monotonic":
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$$\displaystyle a < b \Rightarrow F_{X}(a) < F_{X}(b) $$ (eq5)
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Relaxing strictness

Fig 4.12: Horizontal

This function is also monotonic, but not strictly monotonic. Relax the inequality (4) to the following:
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$$\displaystyle a < b \Rightarrow F_{X}(a) \leqslant F_{X}(b) $$ (eq6) Fig 4.13: Vertical
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Relax further the inequality (4) to the following:

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$$\displaystyle a \leqslant b \Rightarrow F_{X}(a) \leqslant F_{X}(b) $$ (eq7) End proof
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Inverse proposition:
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$$\displaystyle \forall a,\, b \in \Omega$$, if $$\displaystyle F_{X}(a) \leqslant F_{X}(b) $$, then $$\displaystyle a \leqslant b $$. (eq8) Proof Fig 4.14: Increasing monotonicity "Strictly monotonic":
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$$\displaystyle F_{X}(a) < F_{X}(b) \Rightarrow a < b $$ (eq9)
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Relaxing strictness

Fig 4.15: Horizontal

This function is also monotonic, but not strictly monotonic. Relax the inequality (4) to the following:

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$$\displaystyle F_{X}(a) \leqslant F_{X}(b) \Rightarrow a < b $$ (eq10)
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Fig 4.16: Vertical inverse

Relax further the inequality (4) to the following:

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$$\displaystyle F_{X}(a) \leqslant F_{X}(b) \Rightarrow a \leqslant b $$ (eq11) End proof
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Monotonicity of Inverse
Statement II:

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If $$\displaystyle F_{X}(x)$$ is monotonic, then $$\displaystyle F_{X}^{-1}(x)$$ has the same monotonicity. Proof Suppose $$\displaystyle F_{X}(x)$$ is increasing monotonic, then we have
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$$\displaystyle a \leqslant b \Leftrightarrow F_{X}(a) \leqslant F_{X}(b) $$ (eq12)
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For a increasing monotonic function $$\displaystyle F_{X}(x)$$,

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$$\displaystyle a = F_{X}^{-1}[F_{X}(a)] $$ (eq13) and
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$$\displaystyle b = F_{X}^{-1}[F_{X}(b)] $$ (eq14) Substituting Equation( 12 )&( 13 ) into ( 11 ) we have
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$$\displaystyle F_{X}^{-1}[F_{X}(a)] \leqslant F_{X}^{-1}[F_{X}(b)] \Leftrightarrow F_{X}(a) \leqslant F_{X}(b) $$ (eq15)
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This argument is true iff $$F_{X}^{-1}(x)$$ is a monotonically increasing function.

Hence, $$\displaystyle F_{X}^{-1}(x)$$ has the same monotonicity as the original function $$\displaystyle F_{X}(x)$$. End proof

For monotonically decreasing function, these properties also valid.

See also [[media: My_notes_xiu_p15.pdf | my notes on Xiu 2010 p.15]] and [[media: Hailong.2011_10_20_09_15_25.djvu | my notes 2011.10.20]].

Here are [[media: Hailong.2011 10 27 08 21 02.pdf | my notes for 2011.10.27 and 2011.11.03]].

Conclusion 1
Due to the monotonicity of distribution function $$\displaystyle F_X(x)$$, we have
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$$\displaystyle u \leqslant F_{X}(x)\Leftrightarrow F_{X}^{-1}(u)\leqslant x$$ (eq16)
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Proof of Point 2
$$\displaystyle \color{red}{\spadesuit}$$  NEW:

[[media: Hailong.2011 11 10 08 35 29.pdf | My notes for 2011.11.10]], [[media: Hailong.2011 11 17 08 53 10.pdf | My notes for 2011.11.17]], [[media: Hailong.2011 11 24 08 13 27.pdf | My notes for 2011.11.24]], [[media: Hailong.2011 12 01 08 16 35.pdf | My notes for 2011.12.01]],

Special case: Cauchy distribution: Fig 4.17: Cauchy distribution mechanism

Above figure is the probability interpretation of light, in which $$\displaystyle \theta \in [ -\frac{\pi}{2}, +\frac{\pi}{2} ]$$, a random variable with uniform probability distribution function $$\displaystyle f_{\theta}(\theta)$$, $$\displaystyle x $$ a random variable with probability distribution function $$\displaystyle f_x(x)$$ to be determined from $$\displaystyle f_{\theta}(\theta)$$.

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$$\displaystyle x = d\,\tan(\theta) $$ (eq17)
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$$\displaystyle X = d \, \tan(\Theta) $$ (eq18) Sometimes, $$\displaystyle d $$ in eq (17)&(18) can be omitted since $$\displaystyle \,\left | \tan(\pm \frac{\pi}{2}) \right | = \infty $$. Fig 4.18: tangent function
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We define $$\displaystyle \theta (u)$$ is the mapping from $$\displaystyle [0,\,1] $$ to $$\displaystyle [ -\frac{\pi}{2}, +\frac{\pi}{2} ]$$, i.e.,
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$$\displaystyle \theta (u): [0,\,1] \rightarrow [ -\frac{\pi}{2}, +\frac{\pi}{2} ]. $$ (eq19) Then we have
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$$\displaystyle \theta (u) = \pi ( u - \frac{1}{2} ). $$ (eq20) Hence, according to eq (17),
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$$\displaystyle x = \tan(\pi ( u - \frac{1}{2} )) = F_X^{-1}( u ). $$ (eq21) We can solve for $$\displaystyle u $$ from eq (21), as
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$$\displaystyle u = \frac{1}{\pi}\tan^{-1}( x )+ \frac{1}{2} = F_X(x) \in [0,\,1]. $$ (eq22) Fig 4.19: Cauchy cumulative distribution function
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$$\displaystyle \frac{dF_X(x)}{dx} = \frac{du}{dx} = f_X(x) = \frac{1}{\pi}\frac{1}{1+x^2}. $$ (eq23) Fig 4.20: Cauchy probability density function
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temp
General case: The statement of point 2 is equivalent to: Given $$\displaystyle U$$ is uniform in $$\displaystyle (0,1)$$, then$$\displaystyle P_{\mathbf X}(F_{\mathbf X}^{-1}(U) < x) = F_{\mathbf X}(x)$$. From Xiu 2010, p.15 equation 2.7, we already have
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$$\displaystyle F_{X}^{-1}(u) := \text{inf} \{x\mid F_{X}(x) \geqslant u, 0 < u < 1 \}. $$
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Fig 4.21: Left continuity function

By definition of $$\displaystyle F_{X}^{-1}$$, the probability
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$$\displaystyle P_{X}(F_{X}^{-1}(U) < x) = P_{X}(\text{inf} \{y \mid F_{X}(y) \geqslant U \} < x )$$ (eq23)
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For left continuous cdf, for any given $$\displaystyle u$$, we have
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$$\displaystyle F_{X}( \text{inf} \{y\mid F_{X}(y) \geqslant U\}) \leqslant U < F_{X}(x) $$
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In Fig 4.21, that is
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$$\displaystyle \hat u := F_{X}(\hat x)=F_{X}( \text{inf} \{x\mid F_{X}(x) \geqslant \tilde u\}) \leqslant \tilde u < F_{X}(\tilde x) $$ Hence, applying $$\displaystyle F_{X}$$ on both sides of inequality of equation(23), we have $$\displaystyle P_{X}(F_{X}(\text{inf} \{y \mid F_{X}(y) \geqslant U \}) < F_{X}(x))$$ Since $$\displaystyle U $$ is uniformly distributed in $$\displaystyle (0,1)$$, then $$\displaystyle P_{X}(U < F_{X}(x)) = F_{X}(x) $$ (See Fig 4.2)
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For right-continuous cdf, refer to Proof of correctness of Inverse transform sampling method from Wikipedia.

Conclusion 2
If $$\displaystyle U$$ is uniform in $$\displaystyle \left ( 0,1 \right )$$, then $$\displaystyle F_{X}^{-1}(U)$$ has distribution function $$\displaystyle F_{X}$$.

Proof of Point 3
By definition of cdf, we have
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$$\displaystyle P_{X}(X < x) = F_{X}(x)$$ (eq24) Since $$\displaystyle F_{X} $$ is continuous, we can find a unique value $$\displaystyle X$$, such that
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$$\displaystyle X = F_{X}^{-1}(U)$$ (eq25) Substituting equation(25) into equation(24), we can obtain $$\displaystyle P_{X}(F_{X}^{-1}(U) < x) = F_{X}(x)$$. Applying $$\displaystyle F_{X}$$ on both sides, since $$\displaystyle F_{X}$$ is non-decreasing, above equation can be further expressed as $$\displaystyle P_{X}(F_{X}(F_{X}^{-1}(U)) \leqslant F_{X}(x)) = F_{X}(x)$$. That is to say $$\displaystyle P_{X}(U \leqslant F_{X}(x)) = F_{X}(x)$$. It's clearly that $$\displaystyle F_{X}(x) \in \left ( 0,1 \right )$$. Thus, $$\displaystyle F_{X}(x)$$ is uniform in $$\displaystyle \left ( 0,1 \right )$$.
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Conclusion 3
If $$\displaystyle F_{X}$$ is continuous, then $$\displaystyle F_{X}(x)$$ is uniform in $$\displaystyle \left ( 0,1 \right )$$.

Left continuous OR Right continuous
There are two kinds of definitions for cumulative distribution function. The left/right continuity depends on how you define the cdf. Apparently, according to the first definition, cdf is left continuous, while right continuous for the second definition.

Definition I:

Pope 2000, p.38 equation (3.7)
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$$\displaystyle F(V)\equiv P\{ U < V\}$$ (15)
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Kolmogorov 1956, p.23
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$$\displaystyle F^{(x)}(a) = P^{(x)}\{ -\infty, a\} = P\{x < a\}$$ (16)
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"...$$\displaystyle F^{(x)}(a)$$ is continuous on the left."

Definition II:

Xiu 2010, p.9 equation (2.1)
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$$\displaystyle F_{X}(x) = P(X \leqslant x)=P(\{\omega:X(\omega) \leqslant x \}), x\in \mathbb R$$ (17)
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Shao 1999, p.4 equation (1.4)
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$$\displaystyle F(x) = P((-\infty, x ]), x\in \mathbb R$$ (18)
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"$$\displaystyle F$$ is right continuous ..."

Durrett 2010, p.10
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$$\displaystyle F(x) = P(X \leqslant x )$$ (19)
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"$$\displaystyle F$$ is right continuous ..."

Note:

Most of the properties of these two versions of cdf are the same, except one important difference is that definition I is left continuous and definition II is right continuous. See N. Balakrishnan, Valery B. Nevzorov 2003, p.2 or Google books.

Using cdf, we can calculate the probability at any point in the domain as

For left continuous cdf, $$\displaystyle P_X(x) = F_X(x) - F_X(x^-) = 0$$, while $$\displaystyle P_X(x) \neq F_X(x^+) - F_X(x) \neq 0$$.

For right continuous cdf, $$\displaystyle P_X(x) = F_X(x^+) - F_X(x) = 0$$, while $$\displaystyle P_X(x) \neq F_X(x) - F_X(x^-) \neq 0$$.

Verification of left continuity or right continuity
Continuity can be defined in terms of limits of sequences, see Definition in terms of limits of sequences.

Left continuity:

For any sequence $$\displaystyle [x_i]_{i=1,2,...,+\infty} \leqslant \hat x$$ of points in the domain tends to $$\displaystyle \hat x$$ from the bottom, the equivalent $$\displaystyle [f(x_i)]_{i=1,2,...,+\infty}$$ tends to $$\displaystyle f(\hat x)$$, i.e., $$\displaystyle f(x^-) = f(x)$$.

Right continuity:

For any sequence $$\displaystyle [x_i]_{i=1,2,...,+\infty} \geqslant \hat x$$ of points in the domain tends to $$\displaystyle \hat x$$ from the top, the equivalent $$\displaystyle [f(x_i)]_{i=1,2,...,+\infty}$$ tends to $$\displaystyle f(\hat x)$$, i.e., $$\displaystyle f(x^+) = f(x)$$.

For definition I: $$\displaystyle F_X(\hat x) = P_X(X < \hat x)$$

We assume that there is a sequence that satisfy $$\displaystyle x_1 < x_2 < x_3 < ... < x_{+\infty} \leqslant \hat x$$. Since that cdf is non-decreasing, we have $$\displaystyle F_X(x_1) < F_X(x_2) < F_X(x_3) < ... < F_X(x_{+\infty}) \leqslant F_X(\hat x)$$. That's to say $$\displaystyle F_X(\hat x^-) = F_X(\hat x)= P_X(X < \hat x)$$. Hence, $$\displaystyle F_X(x)$$ is left continuous.

Actually, Kolmogorov has proved this statement in Kolmogorov 1956, p.23.

For definition II: $$\displaystyle F_X(\hat x) = P_X(X \leqslant \hat x) = 1 - P_X(X > \hat x)$$

We also assume there is a sequence that satisfy $$\displaystyle x_{+\infty} > ... > x_3 > x_2 > x_1 \geqslant \hat x$$. Any cdf is non-decreasing, we have $$\displaystyle F_X(x_{+\infty}) > ... > F_X(x_3) > F_X(x_2) > F_X(x_1) \geqslant F_X(\hat x)$$, i.e., $$\displaystyle F_X(\hat x^+) = F_X(\hat x)= 1 - P_X(X > \hat x) = P_X(X \leqslant \hat x)$$. Therefore, $$\displaystyle F_X(x)$$ is right continuous.

Inverse of CDF
For strictly increasing continuous cdf, the real number $$\displaystyle F_{X}^{-1}(u), 0<u<1 $$ can be uniquely determined. But in general, the cdf isn't invertible. For this case, we can use generalized inverse cumulative distribution function. Both $$\displaystyle inf$$ and $$\displaystyle sup$$ can be used to define the inverse of cdf.

For left continuous cdf: Fig 5: Left Continuous CDF Define the inverse of cdf as When $$\displaystyle u \in [u_1, u_2]$$
 * {| style="width:100%" border="0"

$$\displaystyle F_{X}^{-1}(u):= inf\{x\mid F_{X}(x) > u\}$$ (20) or
 * style="width:95%" |
 * style="width:95%" |
 *

 * }
 * {| style="width:100%" border="0"

$$\displaystyle F_{X}^{-1}(u):= sup\{x\mid F_{X}(x)  u\}$$ (22) or
 * style="width:95%" |
 * style="width:95%" |
 *

 * }
 * {| style="width:100%" border="0"

$$\displaystyle F_{X}^{-1}(u):= sup\{x\mid F_{X}(x) < u\}$$ (24)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

For right continuous cdf: Fig 6: Right Continuous CDF Define the inverse of cdf as When $$\displaystyle u \in [u_1, u_2]$$
 * {| style="width:100%" border="0"

$$\displaystyle F_{X}^{-1}(u):= inf\{x\mid F_{X}(x) \geqslant u\}$$ (25) or
 * style="width:95%" |
 * style="width:95%" |
 *

 * }
 * {| style="width:100%" border="0"

$$\displaystyle F_{X}^{-1}(u):= sup\{x\mid F_{X}(x) \leqslant u\}$$ (26) When $$\displaystyle u \in [-\infty, u_1) \cup (u_2, +\infty]$$
 * style="width:95%" |
 * style="width:95%" |
 *

 * }
 * {| style="width:100%" border="0"

$$\displaystyle F_{X}^{-1}(u):= \{x\mid F_{X}(x) = u\} = inf\{x\mid F_{X}(x) = u\} = sup\{x\mid F_{X}(x) = u\}$$ (27) Conclusively, for this case, we can define the inverse of cdf as
 * style="width:95%" |
 * style="width:95%" |
 *

 * }
 * {| style="width:100%" border="0"

$$\displaystyle F_{X}^{-1}(u):= inf\{x\mid F_{X}(x) \geqslant u\}$$ (28) or
 * style="width:95%" |
 * style="width:95%" |
 *

 * }
 * {| style="width:100%" border="0"

$$\displaystyle F_{X}^{-1}(u):= sup\{x\mid F_{X}(x) \leqslant u\}$$ (29)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

Useful links
Useful properties of the inverse cdf.

= discussion on 2011.09.08 =

Question 1
$$\displaystyle \mathcal F = \{ \emptyset, { \rm heads}, { \rm tails}, \mathbf\Omega\}$$.

I think the heads and tails should be subsets, it should be designated as $$\displaystyle \{ \rm heads \}$$ $$\displaystyle \{ \rm tails\}$$. Am i right?

Answer 1
Strictly speaking, you can put the curly brackets around "heads" and "tails" to designate that they are singletons (i.e., sets with only one element). But in general it is not necessary to be so strict, since we can write

$${\rm heads} \in \mathcal F $$

or

$$\{ {\rm heads} \} \in \mathcal F $$

Writing style: Don't do a verbatim transcript of my notes; instead use the style of writing wiki articles as shown in the article Gradient_of_vector:_Two_tensor_conventions, i.e., the mediawiki article should read as an article, not lecture notes.


text:
User talk:Kimsonea

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title: User talk:Kimsonea


title: File:Pea1.f11.mtg22.djvu


text:
Motivation and emotion/Book/2011/Learned helplessness

Overview
Upon completion of this chapter you will be able to understand and critique the followings areas:
 * What is Learned Helplessness?
 * Who are the 'founding fathers' in learned helplessness research?
 * What are the main theories?
 * How does learned helplessness develop in animals and humans?

Definitions
Learned helplessness theory defines learned helplessness as individuals who are exposed to events deemed as uncontrollable learn that their associated responses are independent to their outcomes (Alloy, Peterson, Abramson, & Seligman, 1984). As a result of this learning an expectation can form surmising that any response will be pointless (Alloy et al., 1984). This expectation can be generalised to future events or situations and can impact with future learning behaviours (Alloy et al., 1984).

Seligman, Overmier and Maier and learned helplessness in dogs
In 1967, James Overmier and Martin Seligman completed a series of experiments involving inescapable shocks on canine participants (Overmier & Seligman, 1967). The participants were detained in a Pavlovian harness for 24 hours prior to enduring shuttlebox training (Overmier & Seligman, 1967). Initially, the canine participants would react to the shock in the same manner as a ‘normal’ dog. However it was noted that after a period of time the dog would stop removing itself from the shock and remain silent until the shock expires (Overmier & Seligman, 1967). The dog no longer crossed a barrier to escape from shock and instead appeared to submit and yield to the shock (Overmier & Seligman, 1967). Results from further trials showed that the canine participants continued to lack any escape motivation or movement and instead endured severe, continuing shocks in multiple trials (Seligman, Maier & Geer, 1968). During the trials it must be noted that if a canine participant did attempt to escape or displayed signs of avoidance behaviour, this did not necessarily predict future occurrences of escape or avoidance behaviour (Seligman, Maier & Geer, 1968). This was due to the pretreatment of the dogs as they would shortly revert back to their submissive behaviour after escape or avoidance behaviours had occurred (Seligman, Maier & Geer, 1968).

Seligman and Maier's canine experiments
In further experiments on dogs Seligman and Maier (1967) divided dogs into three separate groups. The first group was a control group which received no shocks (Seligman and Maier, 1967). The second group received an electric shock that it could terminate (Seligman and Maier, 1967). The third group received the same shock as the second group however the termination of the shock was dependant on the second group as the third group could not terminate the shock (Seligman and Maier, 1967). To the third group this gave the illusion that the shocks were stopping at random when they were actually being terminated by the second group (Seligman and Maier, 1967). The third group which had no control over the shocks were said to receive ‘inescapable shocks’ (Seligman and Maier, 1967).

Following this initial phase of experimentation all three groups were placed in a shuttlebox which is designed to invoke an escape response resulting from an electric shock (Seligman and Maier, 1967). Resulting from the first phase of experimentation the only dogs that appeared to display a poor escape response were those in the third group (Seligman and Maier, 1967). Due to the inescapable shocks present in the first phase, the dogs in the third group did not try to escape the shock (Seligman and Maier, 1967). Instead they appeared to submit to the shock and passively accept them (Seligman and Maier, 1967). The control group and the second group both appeared to escape the shocks by jumping over the partition in the shuttlebox (Seligman and Maier, 1967). As the control group and the second group both displayed an escape response triggered by the shock, Seligman and Maier both suggested that it was a ‘perceived inescapability’ of the shocks that resulted in the submission or passive acceptance and not the shock itself (Seligman and Maier, 1967).

This submissive response produced by the previous inescapable shocks is quite negative and inhibits normal adaptive behaviours (Seligman, Maier & Geer, 1968). A dog that had not been previously exposed to inescapable shock will endure minimal shock prior to escape (Seligman, Maier & Geer, 1968). Conversely, a dog that is exposed to inescapable shock prior to entering shuttlebox training will take prolonged periods of shock and in some cases will submit to the shock until the shock expires (Seligman, Maier & Geer, 1968). It was at this stage that the term ‘learned helplessness’ had yet to be coined. Overmier and Seligman hypotheses designed to explain similar occurrences. Namely, they considered the competing motor response hypothesis and an adaptation hypothesis (Seligman & Maier, 1968). The competing motor response hypothesis was first discussed by Carlson and Black (1960) which stated that whilst a dog was harnessed it will learn that some motor response will lessen shock. When a dog is placed in a shuttlebox, the dog will utilize this response and not that of jumping the barrier (Carlson & Black, 1960). This hypothesis was found to be false (Overmier & Seligman, 1967). The adaptation hypothesis was first discussed by MacDonald (1946) in which the conclusion that dogs adapted to shock while harnessed and consequently were not motivated to escape shock whilst in a shuttlebox was postulated. This hypothesis was shown to be inconsistent with the findings of Overmier and Seligman (1967).

An analysis of the responses with regard to ‘learned independence’ between shock termination and instrumental learning was considered by Seligman and Maier (1967). It was postulated that whilst harnessed during a period of inescapable shock the dogs learned that shock expiration took place separately to their responses (Seligman & Maier, 1967). It is publicized that typical learning theory permits the notion that animals are susceptible, and on some level ‘aware’, of the probability of shock termination issued by a given, specified response (Seligman & Maier, 1967; Seligman & Maier, 1968). Furthermore, it is also consistent within the literature that animals are also susceptible to the probability of shock termination not issued by a given, specified response (Seligman & Maier, 1967; Seligman & Maier, 1968). Therefore, when particular cases in which these two possibilities are equal it is suggested within the literature that the animal amalgamates the two events (Seligman & Maier, 1967; Seligman & Maier, 1968). To put it rather bluntly, this amalgamation could be labeled an anticipation that shock termination is independent of responding (Seligman & Maier, 1967; Seligman & Maier, 1968).

Affects on behaviour
The earlier experiments conducted by Seligman and his colleagues helped to establish a model of learned helplessness that considered both human and animal behaviours (Overmier & Seligman, 1967; Seligman & Maier, 1967). Once these experiments were published and reviewed there was a period of intense research involving learned helplessness in animals in addition to experiments on humans. Seligman (1978) criticised the formally proposed animal model of learned helplessness and suggested a reformulated model of human depression. It was noted that the new term of reformulation was used as a way to express the importance and relevance of past research and the impact and prevalence this research has on all future studies (Abramson, Seligman, & Teasdale, 1978). This new term and the associated research suggested that learned helplessness in animals could be linked to clinical depression in human beings (Abramson et al., 1978). However this result was supported by a chain of disputable notions. Kathryn Hahner (1989) argued that the reformulated model of depression in humans relied on information and research gathered from the study of animals. This information and research used factors that could not be studied accurately in animals and therefore the reformulation could not be accurately derived from the animal model (Hahner, 1989). Consequently, learned helplessness as a model for human depression has since been discarded (Hahner, 1989).

Seligman (1978) discussed his theory that learned helplessness in animals was parallel to that of human depression. It was suggested by Pratt (1980) that the canine participants of Seligman and Maier’s experiments did not act as through they were suffering from depression, but rather as though they were trauma victims. The experiments conducted by Seligman and Maier all involve the following hypotheses in explanation for the behaviour of the canine participants. Firstly, the dogs may have been incapacitated with heightened levels of anxiety or fear (Hahner, 1989). Another explanation is that the dogs learned that the electric shocks administered during the experiment were inescapable and that all efforts of escape are in vain. Regardless of which explanation is correct, neither account for nor allude to depression in humans.

Fernand Gobet's learned helplessness experiment in chess players
In an experiment conducted by Gobet (1992), the effects of non-contingency between subjects relating to responses and outcomes was observed. The experiment consisted of three groups. The first group was required to solve multiple chess problems with objective solutions and they would consequently receive unaltered, honest feedback on their solutions (Gobet, 1992). The second group was subjected to chess related problems with no objective solutions and received the same feedback as the member of the first group that they were ‘yoked’ with; however there was no control (Gobet, 1992). The final group received a waiting task (Gobet, 1992). It was discovered that the group with the unsolvable chess problems were more depressed than the two other groups at the completion of the experiment (Gobet, 1992). The results of the study limit the area of applicability to that of the learned helplessness model in humans (Gobet, 1992).

How to overcome learned helplessness
In order to overcome learned helplessness it is important to understand how the concept became a reality. By taking steps to reduce a stress response can be the first cornerstone in reversing the affects of learned helplessness in humans. Secondly, by taking control of the environment and developing a positive outlook can reduce the affects of learned helplessness and reverse the learning process of the better. It is important to note that the ability to overcome learned helplessness in humans does not rest solely on the notion of positive thinking, but instead relies on ones ability to challenge the negative outlook and beliefs that were instilled upon conception. As was discussed by Seligman et al. (1968), it is common for people to blame themselves when negative things occur to them. He also discussed the idea that people typically believe that due to a singular negative event in ones life, this one event and the negativity surrounding it can become persistent and infect all areas of ones life (Seligman et al., 1978). Furthermore, he suggested that due to this one negative event this area of life is flawed in an irreconcilable manner and doomed for any future attempts at repair (Seligman et al., 1978). By challenging these three notions, it is possible to overcome learned helplessness and learn to overcome the associated negativity (Seligman et al., 1978). For more information, see Overcoming learned helplessness (Book chapter, 2015).

Criticisms
In 1976, Maier and Seligman discussed other descriptions of the learned helplessness response in animals. Both Maier and Seligman attempted to refute the competing theories of the time however it became aware to them that the learned helplessness phenomenon may have been somewhat confusing (Maier & Seligman, 1976), especially with regard to a standardised, uniformly accepted definition. Consequently, the animal model of learned helplessness was deserted. This decision was considered appropriate by the scientific community largely due to the difficulties and risky assumptions involved with the assessment of animals and their emotional and motivational states (Hahner, 1989).

A significant criticism of learned helplessness can be found in the area of human participants. According to Abramson, Seligman and Teasdale (1978) they had formed a human counterpart to the animal model of learned helplessness. In notable learned helplessness human experiments by Hiroto (1974) and Barber and Winefield (1986), participants were exposed to loud noises as opposed to the shock administered to their animal counterparts. According to the participants they described their apparent submission as simply ignoring the noise (Barber and Winefield, 1986). When contrasted with the animal shock experiments it was apparent that the shocks were painful, however there is no way that one can ever accurately know the psychological basis for learned helplessness in animals and therefore can not be considered similar to the human experiments (Barber and Winefield, 1986).

Conclusions
From the conceptualization of learned helplessness theory progressing through the numerous stages and resting upon the reformulated model it is clear there are many concerns. Initially, it was speculated that helpless animals perceived non-contingent events (Hahner, 1989). It was then decided that learned helplessness in human counterparts was equal to that in animals (Hahner, 1989). Furthering this stretch, it was then suggested that the human model of learned helplessness was equal to that of the human model of depression (Hahner, 1989). Lastly it was concluded that the basis for which their findings were established, namely animal based research, would provide a foundation for a reformulated model of depression in humans (Hahner, 1989). In Seligman’s 1978 publication, he specifically states himself that learned helplessness is a hypothetical construct. As is evident by the variations of the theory presented over the years preceding the 1960’s experiments, the findings will almost certainly have low construct validity. As was argued by Hahner (1989), the Seligman approach to learned helplessness theory and its measurement may be precise, however the issue remains in establishing what is actually being tested.


text:
Monetary Circuit Model/Profits

In this lesson, we will derive the income of capitalists - profits - in our simple economy. We do this by assuming a constant wage share of surplus. In more advanced models, this assumption is relaxed and wage share can vary cyclically.

(My knowledge of this topic is somewhat shaky. Steve Keen's papers omit a lot of explanation of this area, so my interpretation may not be 100% correct. Corrections are welcome.)

Surplus here is in the Sraffian sense of revenues minus direct costs (not including labour) for each individual firm.

The "wage rate", fwr, paid by firms depends on two factors. First is the wage share received by workers, 1 - σ, where σ (sigma) is the share of surplus going to capitalists. Second is the turnover period, τ (tau), the length of time it takes for the firm to recoup its initial investment in production. The initial investment is the stock of firm deposits, fd. If we take the inverse of the turnover period, 1/τ, we have the number of times the firm recoups on its initial investment in a year. Multiplying this by the initial investment, fd, gives the firm revenue over the course of a year and multiplying this again by the wage share, 1- σ, gives the wage bill. Since the wage bill is also given by fwr*fd, we can derive τ from fwr and an assumed wage share:

$$ fwr = \frac{1-\sigma}{\tau} $$

Given our fwr parameter of 2 and an assumed wage share (1 - σ) of 60%, we can calculate τ to be 0.3. Since all firm revenue that does not go to wages is distributed as profit (Π), we can now determine it using τ (turnover period) and σ (profit share):

$$ \Pi = \frac{\sigma}{\tau}F_d $$

The result (plus interest earned on deposits and banker income) is this:

All classes are able to earn a continuous positive income despite a fixed initial stock of money. This is because that initial stock is recycled over and over in the economy - one person's expenditure is another's income.

In the next lesson, we will look at what happens when we apply a shock to the model in the form of a credit crunch.

title: Monetary Circuit Model/Profits


text: Monetary Circuit Model/incomes.py

title: Monetary Circuit Model/incomes.py


text: Monetary Circuit Model/graphing.py

title: Monetary Circuit Model/graphing.py


text: Template:10% done

title: Template:10% done


text:
User talk:Mitchblue006

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User talk:Rafreeman

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User talk:Ajeshderenaissance

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User talk:66.182.213.34

72.194.97.95 21:23, 7 October 2011 (UTC)AAron Kearns,San Clemente CA 92672I think time travel is possible in theory but not in practical use. Time doesn't exist. It is a precetion of the mind only made possible by the gauge with which you use to reference it. For example a days worth of time consists of a single rotation of the earth round the sun. We notice "time" pass because of tasks we complete within this concept of messure. Hence the idea "time" moves faster when we are having fun.

The speed at wich we move governs the time it takes to complete a task. Kenetic energy governs how fast we move. Gravity and the speed of light are a constant. Without either of these properties we would not have a manner inwich to guage, that is compare and contrast, how many things we could do in what we define as a "day" a tangible representation of the concept of time. Do nothing and time becomes meaninless.

And the reason i don't think time travel is possible in the manner in which people contextually think of is because humans would have to do 1 of 2 things. First create a propulsion system capable of getting as close to light speed as possible and then know exactly where every possible celestial body containing any mass is in relation to where you start the engine and how long you let it run for. It is my belief that the spacecraft would smash into an asteriod or planet or another sun and be destroyed. The second way to travel through time with no control whatsoever would be to produce an energy field strong enough to counter gravity. Three problems with this are first countering gravity completely is beyond anything I have heard of, secondly if you do no form the shield exactly evenly odds are you would end up with a thermoneulear explosion by having one atom free of gravity smacking into another atom still under gravitys influence at the speed of the planets rotation. That should be fast enough to cause a fission reaction with the one atoms nucli bonding with the others and kaboom! and the third problem is even if u create the energy field to counter gravity and enclose it around anything it will instentainiouly be struck by an object under gravitys control. Bummer right?

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title: File:Pea1.f11.soccer.field.svg


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User talk:Addismultimedia

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User:Pogostix~enwikiversity

My aim is to research and help others research complex questions of learning such as "Is there a fourth dimension?" or "Are character traits genetic?" or "Is time and place simply a platform for our waking consciousness?" or "What is the highest plane of thought?" or "Is success static?" or "Is social approval an illusion?" or "Can we communicate via thought alone?" or "If all roads lead to Rome where do all the roads lead from - Rome?" or "Does the earth always rotate around its axis in the exact same line from the sun every year?" or "Do we experience cycles of coincidence?"

These philosophical and scientific issues are of greater relevance to our human experience than the mundane, such as buying and selling, working and studying. I believe the more we can understand about the planet we dwell upon, and the complexities of our human minds, the better we can live. Art, Science, Literature, Philosophy and Music intertwine as navigation into a new conceptualization of human experience. Behold!

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User talk:Pogostix~enwikiversity

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Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Pogostix. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Pogostix~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:41, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:18, 19 April 2015 (UTC)

title: User talk:Pogostix~enwikiversity


text:
User talk:Captain-n00dle

 Hello Captain-n00dle, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.
 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
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You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Abd 23:01, 7 October 2011 (UTC)

title: User talk:Captain-n00dle


text:
User talk:Filmfroggie

 Hello Filmfroggie, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.
 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.
 * Follow Wikiversity on twitter (http://twitter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Abd 23:20, 7 October 2011 (UTC)

title: User talk:Filmfroggie


text:
User talk:4T2ud

 Hello 4T2ud, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.
 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.
 * Follow Wikiversity on twitter (http://twitter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Abd 23:21, 7 October 2011 (UTC)

title: User talk:4T2ud


text: File:EGM6341.s11.TEAM1.WILKS EC27.vql.svg


text:
User talk:Wardstaff

 Hello Wardstaff, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.
 * Explore Wikiversity with the links to your left.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.
 * Follow Wikiversity on twitter (http://twitter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Abd 01:50, 8 October 2011 (UTC)

title: User talk:Wardstaff


text:
User talk:UC3025323/The Evolution of Alcohol and Tobacco Sport Sponsorship Agreements

In-text references
Hey I just did some quick referencing changes. Leigh would like the external link included. I hope that helps.


title: File:Pea1.f11.rlc.circuit.svg


title: File:DigitalDesign.20111006.pdf


text:
Wikiversity:Candidates for Custodianship/Abd (Bureaucrat)

 * There is a serious backlog at WV:Changing username. There are only two active bureaucrats, and both appear to busy to handle these requests. As an ordinary user, I studied how these changes are made on other wikis as well as here, reviewed the requests, verified diffs and claims, requested additional information where needed, and made recommendations. I also created templates to make user requests create links for what is needed. However, even with the work simplified in this way, and in spite of repeated requests, no 'crat has had the time to complete the requests. This is a task that should ordinarily be done within a few days. The oldest standing request is from February.
 * Therefore I am volunteering to serve. I understand that my general work on Wikiversity is controversial. However, my actual use of tools as a probationary custodian has not been controversial, as can be seen by a review of my open probationary custodianship at Candidates for Custodianship/Abd (full custodian). The most serious objection is that I, as an ordinary user, sometimes implement ideas in advance of consensus. Of course, any user may do this! I always understood this as the basic wiki concept.
 * In this case, I'm suggesting something new: probationary bureaucratship, requiring a mentor, who should be a bureaucrat. If this is allowed, and as a probationary 'crat, I would refrain from all use of 'crat tools except under the following circumstances:
 * Changing username and usurpations, having first reviewed the application and having made a recommendation, which stands for at least a week without opposition from any custodian. Any user may, of course, request that a custodian intervene.
 * Other usage with the specific on-wiki approval of another bureaucrat.
 * Reviewing other bureaucrat nominations, only if another local 'crat is not available for at least 35 days after the start of !voting. This is only a contingency that all 'crats are completely unavailable, that's unlikely. Similarly, under this contingency, I would only use 'crat tools with clear, demonstrated, on-wiki consensus, allowing me to do so, pending the creation of new full 'crats.
 * Until and unless I become a "full bureaucrat," any custodian may request removal of the 'crat bit by a steward at meta, based on diff'd violation of the above terms. I will resign at meta as soon as possible upon the request of the mentor, regardless of "cause," and the mentor may also immediately request removal at meta of the privilege, anticipating that resignation.
 * No bureaucrat action would be taken in anticipation of controversy. This is only intended to handle non-controversial tasks, assisting the existing bureaucrats.
 * Because of the nature of this request, and because of the shortage of 'crats, I am suggesting that, in this case, the mentor 'crat may accept and implement, setting whatever conditions or restrictions seen fit. In a sense, the title of this position might be "assistant bureaucrat," serving at the pleasure of the mentor, and extending the working capacity of the mentor.
 * Are there any other users who might consider volunteering? Any with 'crat experience? --Abd 14:58, 8 October 2011 (UTC)

Comments

 * Abd, I'm sorry to say this, because in many ways you are a great custodian, but I think the shortage of 'crats should be dealt with by the promotion of a non-probationary custodian, who has the absolute trust of the community. I would however, be happy to let you be given 'crat tools for a day or two to deal with the username change backlog. --S Larctia 18:16, 8 October 2011 (UTC)
 * That's up to the implementing 'crat, who can state that it is for a limited period. Fine with me. However, what I'll point out is that this would essentially create more work for the stewards, without necessity. Not a lot, though. If a non-probationary custodian volunteers or is nominated, we are still looking at a possible month before we'd have a new 'crat, given what's happened before. --Abd 18:27, 8 October 2011 (UTC)
 * There has not been community consensus to give you unsupervised indefinite access to administrative tools. I doubt there will be community consensus to give you supervised indefinite access to 'crat tools. The possible consequences of a user abusing 'crat tools are enormous: many 'crat actions can't be as easily reversed as administrative actions, and it would give you more power than custodians who have the unanimous support of the community. --S Larctia 18:59, 8 October 2011 (UTC)

 * While the username change request blacklog could be due to the bureaucrats being too busy, it could also be due to uncertainty as to when or even if the Wikiversity community considers it appropriate to usurper usernames. People have attempted to discuss the issue without any definitive resolution, which even when the bureaucrats are not busy has sometimes resulted in no action being taken unless the name requested was never registered. Some people have felt strongly that giving a registered username to somebody else is a failure to assume good faith. -- dark lama  19:06, 8 October 2011 (UTC)
 * I certainly believe that usurpation should not occur if the registered user has made any edits. There are complicated decisions to be made concerning individual cases. --S Larctia 19:42, 8 October 2011 (UTC)
 * If there were no 'crats on Wikiversity, all of these changes would be routinely handled by stewards. If there is a problem with any change or usurpation, it would be appropriate to object on the Changing username page, not just deny the requests with a pocket veto. There has been discussion of the usurpation issue. No consensus appeared. The present situation is untenable: we have a stated policy, we have a request page, but nobody is handling the requests, either to approve or to deny. That wastes users' time and it's a scandal at meta. As to "power," well, if I violated the terms here, I'd be history quickly. But, hey, I really don't care, personally. If there is a permanent custodian willing to volunteer like this, under similar conditions as I've proposed for myself, I'd certainly support it, more easily than permanent 'cratship, for *any* custodian. Darklama, how about you?
 * Meanwhile, if there are any problems with any of my recommendations on the standing requests, surely a responsible user here will comment and point them out. The recommendations have been sitting for over a month. --Abd 23:39, 8 October 2011 (UTC)
 * Abd, why didn't you ask a steward on meta to sort out the backlog ? It doesn't look like such a lot of work to remove it, and it wouldn't be controversial for them to get involved as the 'crats here obviously don't have the time to do it. Simone  12:00, 9 October 2011 (UTC)
 * The stewards can't intervene unless we have a policy (or the equivalent) explicitly saying they can do so. See below. --SB_Johnny talk 23:35, 10 October 2011 (UTC)
 * Indeed. It would have been rather less drama if we'd discussed doing this on the colloquium or elsewhere rather than going through with this nomination for a position which doesn't exist. I'm pretty sure there would be community consensus for stewards to deal with this sort of thing, simply because most of the usurption requests aren't really to do with Wikiversity editors, but more to do with wikimedia users trying to get "perfect" unified logins. -- Simone 09:46, 13 October 2011 (UTC)

 * Abd, you're currently a probationary custodian, and perhaps you shouldn't be. You are not a "full" custodian because there was no consensus to put you in that position. If we were to create the position of "probationary 'crat", we'd need to discuss it first. Also, if the backlog really bothers you, bring it up on the colloquium for discussion. For the record, another probationary custodian (User:Thenub314) happens to be a 'crat on Wikibooks (userpage), so if this is an emergency (and I'm not convinced that it is), he would be by far a more suitable candidate than someone who is clearly not quite trusted by the community. --SB_Johnny talk 22:13, 8 October 2011 (UTC)
 * Sure, though Thenub314 has been seriously inactive, both here and on Wikibooks. Nevertheless, I'd support it. "Perhaps shouldn't be" a probationary custodian? Perhaps, but, on the other hand, perhaps I should be a permanent custodian, but I elected to accept your proposal for continued probationary status in order to resolve the issue without unnecessary contention. I can push buttons as a probationary custodian as easily as a permanent one. My proposal here would allow me to operate, in a limited way, in full view of the community, plus any additional restrictions (including immediate removal of the bit by the mentor or any 'crat, on request at meta with reference to this discussion, could be added by the mentor. How about you as a mentor, SBJ? --Abd 23:39, 8 October 2011 (UTC)
 * For what it is worth, I am less inactive then edit histories might suggest. I do try to keep an eye on things here and at WB.  Much of my wikimedia time has been more focused on hacking texvc these days.  If you've noticed any new bugs since they rolled out 1.18... that is sadly my fault.  But if you've noticed any improvements (archaic greek characters, \sen finally working, etc) that is also largely my fault. So I spend the majority clicking preview for some test case in a sandbox... usually not logged in.  But overall neither of us is a great choice, better to promote someone who is already a custodian.  Thenub314 03:35, 14 October 2011 (UTC)
 * I definitely vote Darklama for 'crat. (Also, Pedro for President!)
 * Agree that we may need to clarify the policy. Perhaps someone can gather all the material in one place, and put it to a one month vote with the result becoming at least temporary policy?
 * My understanding of the steward situation is that stewards will not intervene where we have local crats. I don't see that as an argument for temporarily removing 'crat flags from inactive crats - just for having more local crats. --Draicone (talk) 16:23, 9 October 2011 (UTC)
 * +1 for Darklama. How about you, Draicone?
 * OTOH, we could also just add a note to the local policy allowing stewards to flip the name in cases where the target account has no edits at all. I'm personally just not comfortable usurping an account that has edits for the sole purpose of unifying a name, particularly when it seems unlikely that the person asking isn't likely to participate here anyway. If the person asking has already made more contributions than the target account, that's a different story. There was a CR about that some time back, and consensus seemed to be on the side of preserving old accounts iirc. --SB_Johnny talk 10:22, 10 October 2011 (UTC)
 * Too busy at the moment. I could do a weekend, but not much more. Maybe next year.
 * I'm happy with explicitly approving steward intervention, but I'm not sure if they'll be happy with that - I suspect part of the policy basis was to avoid burdening stewards. Also, I agree with the concern that we shouldn't just rename accounts for the sole purpose of SUL (unless, of course, WMF tells us to). m:Help:Unified login suggests that renames are "subject to local policy" but also has an underlying theme that the user with the greater claim to a wiki identity gets the username. Perhaps the solution is to simply encourage people to have a look around and make a few edits, improving the wiki and making the decision easier. --Draicone (talk) 13:24, 10 October 2011 (UTC)
 * (edit conflict with below) I've considered asking stewards. Problem is that SBJ did do two recent username requests, one simple name change and one usurpation, where the users asked him directly on his user page.. Stewards will assume that this means we have at least one active 'crat, and are likely to decline. (And I've seen them suggest that if we have inactive 'crats, we should remove the bits.) To me, the biggest problem here is that we have a page for users to request a name change, which implies that we will do this from requests on that page. But mostly, we don't. I went to fr.wikiversity and requested usurpation of Abd there. Took one day. --Abd 00:18, 11 October 2011 (UTC)
 * For the record, I have begged Darklama publicly and on IRC to run for Bureaucrat a few times in the past and he always refused. Ottava Rima (talk) 23:21, 10 October 2011 (UTC)
 * For the record, even if I did accept the Bureaucrat tools, it wouldn't make a difference without at least a temporary usurper policy. -- dark lama  00:09, 11 October 2011 (UTC)
 * We can generate that policy, I would if I had time. We do have existing practice. I'll open an Assembly topic on this, in addition to using existing procedures for policy development. But I can't do this today, for sure. --Abd 15:19, 13 October 2011 (UTC)

 * To be explicit, none of the pending usurpation requests involve a target username with edits. Review of the old discussions shows some sentiment -- with practically no support -- on keeping old usernames even without edits, but it's not at all clear that this was carefully considered. Debate was mostly over what appears to have been a totally theoretical situation: a requested usurpation of an account which has edits. That is apparently rare, rare enough that it might be foolish to declare a policy. I agree with SBJ that we could explicitly allow usurpation of no-edit accounts, given certain considerations. If I'm correct, only one user may have an SUL account with a given name. I'd personally want to see real examples before pulling policy out of thin air, or some other place. --Abd 18:59, 10 October 2011 (UTC)
 * It's not "theoretical", Abd: the CR came about because there was such a case (and I know there were a few more as well). If you want to start another CR on the narrow issue of letting the stewards push the buttons on what are generally not local issues anyway, I'd support it, and I'm sure it would pass with flying colors.
 * Just for the benefit of those who don't understand the problem: Single User Login (SUL) was put in place only a couple years ago, and probably should have been put in place long before then. The SUL problems really only become problems when there are very old accounts that use a name that might also have been used on another WMF wiki. I hope that makes sense. --SB_Johnny talk 23:35, 10 October 2011 (UTC)
 * Thanks for clarifying this for others, SBJ. However, I'd looked for examples. You are referring to Community Review/Usurpation of usernames, which appears to have arisen out of discussion on Wikiversity talk:Changing username which was raised as a theoretical question, and I've found no reference on either page to an actual case in dispute. Usurpations have been routinely handled, including a recent one by you, SBJ. If the CR was based on an actual case, nobody bothered to mention it. Reviewing Mu301's edits around that time, I found User_talk:Little_Lewis. This would have been a request for a usurpation where the target account had many edits. Apparently it never became one, it was withdrawn. This was explained at . Little Lewis was successful at usurpation on en.wiki, where an account named Lewis had no edits and is now Lewis (usurped). This may or may not have been our User:Lewis.
 * It is obvious from many examples that we have a defacto policy of not denying applications for usurpation where the target account has no edits and the other niceties are satisfied. Darklama, there is a "policy" to follow, existing practice. --Abd 00:46, 11 October 2011 (UTC)
 * Abd, the CR was indeed started because of a particular case, see User:Doug's contribs for details.
 * It's rather annoying to be accused of dishonesty for no particular reason here. I was there, so I remember. You weren't, so you don't remember. --SB_Johnny talk 19:51, 12 October 2011 (UTC)
 * SBJ, I do not suspect and have not accused you of dishonesty. I've noted that reference to a precipitating case was missing, and you had not, until now, supplied it.
 * This is the case. That's appalling, SBJ. User:BewareofDoug filed the request on 2 December 2008. The request seems to have sat there until 30 August 2009, when Mikeu asked BewareofDoug about emailing the target user (and an apparent sock of the user). BewareofDoug responded the same day. Nothing was done until Jtneill finally did the usurpation on 12 February, 2011. The CR was never closed. Over three years to handle what should be a relatively routine request.
 * BewareofDoug did participate in the discussions. In any case, the Doug case shows that a usurpation can be done even if the usurped account has edits. Nobody complained about it. And all of this is a red herring. The current usurpation requests do not involve any target account with edits. So even this supposedly "controversial" case was ultimately uneventful. The original discussion at Wikiversity_talk:Changing_username was started on purely theoretical grounds, it seems, as I noted.
 * Doug, by the way, is a sysop on en.wiki. Perhaps our extreme bureaucratic inefficiency is part of our outreach program? --Abd 22:53, 12 October 2011 (UTC)
 * It's not appalling, there was simply no local consensus to allow somebody's name (with contribs) to be usurped. I have no idea why it was done in the end at all, since the various discussions prior to that (and there were others on the colloquium and elsewhere over the years) seemed to lean against it. Simply making a policy one way or another is what needs to be done.
 * Again, since the vast majority of the requests seem to come from people who just want to have a "perfect" SUL, rather than to consolidate their contributions here with their contributions elsewhere, perhaps it's better to let meta handle those. --SB_Johnny talk 23:14, 12 October 2011 (UTC)
 * Then we should have instructions on Changing username to reflect our actual practice and so that users don't waste their time. However, we do have actual practice, usurpation is not seriously controversial when there are no edits in the target account, and no sustained objections have been raised in any real situation. It is just totally unreliable, the lack of attention from 'crats is obvious. This is the problem with those discussions: hardly anyone is paying attention to them. This whole procedure was backwards. Real case (Doug): practically no discussion. Hypothetical situation: wasted inconclusive discussion.
 * Just noticed. Your comment here, SBJ, was unbecoming of a bureaucrat. This is not looking good. --Abd 23:05, 12 October 2011 (UTC)
 * I'm not really sure what bearing that has to do with this situation. -- Simone 09:54, 13 October 2011 (UTC)
 * Just sayin.' Briefly. It's related, because it shows the attitude of one bureaucrat, which is certainly having an impact on cleaning up the mess at Changing username, which was the occasion for this candidacy. My candidacy was a long shot, intended as much to call attention to the need, in the hopes that a permanent custodian would volunteer. There are other possible solutions, that won't be decided here. I'll confine myself to saying that, had we behaved more responsibly, as a community, with respect to the applications made, it's likely we'd have garnered additional user participation. There is a lot of need for coordination with Wikipedia, and we've been needlessly irritating Wikipedia administrators, instead of making them feel welcome. That increases the attitude among WMF volunteers in general that Wikiversity is unreliable and flaky. --Abd 15:19, 13 October 2011 (UTC)

 * Strong oppose - Plus, there is no such thing as a "Bureaucrat mentorship", so putting that down there shows that you are further unqualified. You aren't even an actual admin/custodian, so you definitely don't have any right to ask for Bureaucratship. Ottava Rima (talk) 23:19, 10 October 2011 (UTC)
 * If my suggestion that there may be such a possibility as "probationary bureaucratship" disqualifies me, then, indeed, I'd be disqualified. And if the community prefers no 'crats (in effect or in actuality) to a probationary crat, perhaps one who may be restrained by any custodian (as per, say, something like Candidates for Custodianship/Standard stop agreement), then, again, no problem. Easily, my work as a 'crat could be subject to very tight restrictions, simply allowing me to do certain specified actions, with violation of that resulting in immediate removal of the privilege. However, I'm in no rush, I'm just not withdrawing this candidacy because no other workable alternative has been proposed. --Abd 23:40, 25 October 2011 (UTC)

 * The difficulty is that the community has not trusted you with full custodial rights, but as a 'crat you can add full custodians, 'crats, etc. Once done this is not something that can be undone locally.  So it is rather different then a probationary custodianship, in that other custodians that disagree with you can undo your actions.  Given WV's history for drama, I think this is not a good idea. Thenub314 02:03, 26 October 2011 (UTC)


text: User talk:Kagogathoni

title: User talk:Kagogathoni


text:
History Essay Format & Thesis Statement

Thesis Statement
A thesis statement is generally a single sentence (The last sentence of Intro) within the introductory paragraph of the history (or thesis) essay, which makes a claim or tells the reader exactly what to expect from the rest of the text. It may be the writer's interpretation of what the author or teacher is saying or implying about the topic. It may also be a hypothesis statement (educated guess) which the writer intends to develop and prove in the course of the essay.

The thesis statement, which is in some cases underlined, is the heart of a history or thesis essay and is the most vital part of the introduction. The assignment may not ask for a thesis statement because it may be assumed that the writer will include one. If the history assignment asks for the student to take a position, to show the cause and effect, to interpret or to compare and contrast, then the student should develop and include a good thesis statement.

Following the introductory paragraph and its statement, the body of the essay presents the reader with organized evidence directly relating to the thesis and must support it.

It's a summarized writing about what you're talking about and why who what where when or how.

Characteristics of a great thesis statement
 * Is a strong statement or fact which ends with a period, not a question.
 * Is not a cliché such as “fit as a fiddle”, “time after time”, “a chain is only as strong as its weakest link”, “all in due time” or “what goes around comes around”.
 * Is not a dictionary definition.
 * Is not a generalization.
 * Is not vague, narrow or broad.
 * States an analytic argument or claim, not a personal opinion or emotion.
 * Uses clear and meaningful words.
 * Don't overuse a topic.
 * Try to use many different information.
 * Don't say something boring like "today im going to tell you yada yada yada"
 * Start with a hook then back it up with informations

The History Essay Format
Essay is an old French word which means to “attempt”. An essay is the testing of an idea or hypothesis (theory). A history essay (sometimes referred to as a thesis essay) will describe an argument or claim about one or more historical events and will support that claim with evidence, arguments and references. The text must make it clear to the reader why the argument or claim is as such.

Introduction

Unlike a persuasive essay where the writer captures the reader's attention with a leading question, quotation or story related to the topic, the introduction in a history essay announces a clear thesis statement and explains what to expect in the coming paragraphs. The Introduction includes the key facts that are going to be presented in each paragraph.

The following phrases are considered to be poor and are normally avoided in the introduction: “I will talk about”, “You will discover that”, “In this essay”, “You will learn” or other such statements.

Body (Supporting Paragraphs)

The paragraphs which make up the body of a history essay offers historical evidence to support the thesis statement. Typically, in a high school history essay, there will be as many supporting paragraphs as there are events or topics. The history teacher or assignment outline may ask for a specific number of paragraphs. Evidence such as dates, names, events and terms are provided to support the key thesis.

The topic sentence tells the reader exactly what the paragraph is about. Typically, the following phrases are never part of a topic sentence: “I will talk about”, “I will write about” or “You will see”. Instead, clear statements which reflect the content of the paragraph are written.

The last sentence of a supporting paragraph can either be a closing or linking sentence. A closing sentence summarizes the key elements that were presented. A linking sentence efficiently links the current paragraph to the next. Linking can also be done by using a transitional word or phrase at the beginning of the next paragraph.

Conclusion

In the closing paragraph, the claim or argument from the introduction is restated differently. The best evidence and facts are summarized without the use of any new information. This paragraph mainly reviews what has already been written. Writers don't use exactly the same words as in their introduction since this shows laziness. This is the author's last chance to present the reader with the facts which support their thesis statement.

Quotes, Footnotes and Bibliography
Quotes

Quotations in a history essay are used in moderation and to address particulars of a given historical event. Students who tend to use too many quotes normally lose marks for doing so. The author of a history essay normally will read the text from a selected source, understand it, close the source (book for web site for example) and then condense it using their own words. Simply paraphrasing someone else’s work is still considered to be plagiarism. History essays may contain many short quotes.

Quotations of three or fewer lines are placed between double quotation marks. For longer quotes, the left and right margins are indented by an additional 0.5” or 1 cm, the text is single-spaced and no quotation marks are used. Footnotes are used to cite the source.

Single quotation marks are used for quotations within a quotation. Three ellipsis points (...) are used when leaving part of the quotation out. Ellipsis cannot be used at the start of a quotation.

Footnotes

Footnotes are used to cite quotation sources or to provide additional tidbits of information such as short comments.

Internet sources are treated in the same way printed sources are. Footnotes or endnotes are used in a history essay to document all quotations. Footnotes normally provide the author's name, the title of the work, the full title of the site (if the work is part of a larger site), the date of publication, and the full URL (Uniform Resource Locator) of the document being quoted. The date on which the web site was consulted is normally included in a footnote since websites are often short-lived. Bibliography

Unless otherwise specified by the history teacher or assignment outline, a bibliography should always be included on a separate page which lists the sources used in preparing the essay.

The list is always sorted alphabetically according to the authors’ last name. The second and subsequent line of each entry of a bibliography is indented by about 1 inch, 2.5 cm or 10 spaces.

A bibliography is normally formatted according to the “Chicago Manual of Style” or “The MLA Style Manual”.

Plagiarism
History and thesis essay writers are very careful to avoid plagiarism since it is considered to be a form of cheating in which part or all of someone else’s work is passed as one’s own. Useful guidelines to help avoid plagiarism can be found in the University of Ottawa document "Beware of Plagiarism".

Formatting Requirements

 * Letter-sized 8.5”x11” or A4 plain white paper
 * Double-spaced text
 * 1.5” (3 cm) left and right margins, 1” (2.5 cm) top and bottom margins
 * Regular 12-point font such as Arial, Century Gothic, Helvetica, Times New Roman and Verdana
 * A cover page with the course name, course number, group number, essay title, the teacher’s name, the author's name, the due date and optionally, the name of the author's school, its location and logo
 * Page numbers (with the exception of the cover page)
 * No underlined text with the exeception of the thesis statement
 * No italicized text with the exception of foreign words
 * No bolded characters
 * No headings
 * No bullets, numbered lists or point form
 * No use of the these words: “Firstly”, “Secondly”, “Thirdly”, etc.
 * Paragraph indentation of approximately 0.5 inch, 1 cm or 5 spaces
 * Formatting according to the “Chicago Manual of Style” or the “MLA Style”.

Basic Essay Conventions

 * Dates: a full date is formatted as August 20, 2009 or August 20th, 2009. The comma and the “th” separate the day from the year.
 * Dates: a span of years within the same century is written as 1939-45 (not 1939-1945).
 * Dates: no apostrophe is used for 1600s, 1700s, etc.
 * Diction: a formal tone (sophisticated language) is used to address an academic audience.
 * Numbers: for essays written in countries where the metric system is used (e.g., Europe, Canada), no commas are used to separate groups of three digits (thousands). For example, ten thousand is written as 10 000 as opposed to 10,000.
 * Numbers: numbers less than and equal to 100 are spelled out (e.g., fifteen).
 * Numbers: round numbers are spelled out (e.g., 10 thousand, 5 million).
 * Numbers: for successive numbers, digits are used (e.g., 11 women and 96 men).
 * Percentages: the word “percent” is used instead of its symbol % unless listing successive figures. When listing many figures, the % symbol is also used.
 * Pronouns: the pronoun “I” is not used since the writer does not need to refer to him/herself unless writing about “taking a position” or making a “citizenship” statement.
 * Pronouns: the pronoun “you” is not used since the writer does not need to address the reader directly.
 * Tone: in a history or thesis essay, the writer does not nag, preach or give advice.

Use of Capital Letters
A history or thesis essay will make use of capital letters where necessary.

 * Brand names, trademarks or product names
 * First word of a direct quotation
 * First word of a sentence
 * Name or title of a book, disc, movie or other literary works
 * Names of distinctive historical periods (e.g., Middle Ages)
 * Names of festivals and holidays
 * Names of languages (e.g., English, French)
 * Names of school subjects, disciplines or specialties are not capitalized unless they happen to be the names of languages
 * Names of the days of the week and of the months of the year (e.g., Monday, January)
 * Pronoun I (e.g., “Yesterday, I was very happy.”)
 * Proper names (e.g., John Smith, Jacques Cartier)
 * Religious terms (e.g., God, Sikhs)
 * Roman numerals (e.g., XIV)
 * Words that create a connection with a specific place (e.g., French is capitalized when it is used in the context of having to do with France)
 * Words that identify nationalities, ethnic groups or social groups (e.g., Americans, Canadians, Loyalists)

Miscellaneous Characteristics

 * A word processor such as Microsoft Word or a free downloadable processor such as Open Office could be used to format and spell-check the text.
 * An essay plan or a graphic organizer could be used to collect important facts before attempting to write the essay.
 * Correct use of punctuation; periods, commas, semicolons and colons are used to break down or separate sentences.
 * Paragraphs are not lengthy in nature.
 * Street or Internet messaging jargon such as “a lot”, “:)”, “lol” or “bc” is not used.
 * Text that remains consistent with the thesis statement.
 * The essay has been verified by a peer and/or with the word processor's spell-check tool.
 * The same verb tense is used throughout the essay.

title: History Essay Format & Thesis Statement


text:
User talk:January

 Hello January, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

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You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Abd 18:16, 8 October 2011 (UTC)

History Essay Format & Thesis Statement
Transwiki'd. Please inform the Wikipedia community, that's something I can't do unless by email (unreliable) or ban evasion (only for emergencies or strong w:WP:IAR, which certainly doesn't apply here). Let me know if there is anything else I can do. --Abd 18:16, 8 October 2011 (UTC)

title: User talk:January