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Silver Spring, Maryland

Silver Spring is a census-designated place (CDP) in southeastern Montgomery County, Maryland, United States, near Washington, D.C. Although officially unincorporated, it is an edge city with a population of 81,015 at the 2020 census, making it the fifth-most populous place in Maryland after Baltimore, Columbia, Germantown, and Waldorf.

Downtown Silver Spring, located next to the northern tip of Washington, D.C., is the oldest and most urbanized area of Silver Spring, surrounded by several inner suburban residential neighborhoods inside the Capital Beltway. Many mixed-use developments combining retail, residential, and office space have been built since 2004.

Silver Spring takes its name from a mica-flecked spring discovered there in 1840 by Francis Preston Blair, who subsequently bought much of the area's surrounding land. Acorn Park, south of downtown, is believed to be the site of the original spring.

Geography
As an unincorporated census-designated place, Silver Spring's boundaries are not consistently defined. As of the 2010 census, the U.S. Census Bureau gives Silver Spring a total area of 7.92 sqmi, which is all land; however, the CDP contains some creeks and small ponds. This definition is a 15% reduction from the 9.4 sqmi used in previous years.

Silver Spring contains the following neighborhoods: Downtown Silver Spring, East Silver Spring, Woodside, Woodside Park, Lyttonsville, North Hills Sligo Park, Long Branch, Indian Spring, Goodacre Knolls, Franklin Knolls, Montgomery Knolls, Clifton Park Village, New Hampshire Estates, and Oakview.

The U.S. Geological Survey, U.S. Postal Service, Silver Spring Urban Planning District, and Greater Silver Spring Chamber of Commerce, each use their own slightly different definitions. The Postal Service in particular assigns Silver Spring mailing addresses to a large swath of eastern Montgomery County sometimes called "Greater Silver Spring", including Four Corners, Woodmoor, Wheaton, Glenmont, Forest Glen, Forest Glen Park, Aspen Hill, Hillandale, White Oak, Colesville, Colesville Park, Cloverly, Calverton, Briggs Chaney, Greencastle, Northwood Park, Ashton, Sandy Spring, Sunset Terrace, Fairland, Lyttonsville, Kemp Mill, a portion of Langley Park, and a portion of Adelphi. The area that has a Silver Spring mailing address is larger in area than any city in Maryland except Baltimore.

Landmarks in the downtown area include the AFI Silver Theatre, the National Museum of Health and Medicine, a branch of The Fillmore, and the headquarters of the National Oceanic and Atmospheric Administration. Greater Silver Spring includes the headquarters of the Seventh-day Adventist Church, the Food and Drug Administration, and the Ahmadiyya Muslim Community in the U.S.

Parks and recreation
Four major creeks run through Silver Spring: from west to east, they are Rock Creek, Sligo Creek, Long Branch, and Northwest Branch. Each is surrounded by parks offering hiking trails, playgrounds, picnic areas, and tennis courts. On weekends, roads are closed in the parks for bicycling and walking.

Northwest Branch Park also includes the Rachel Carson Greenway Trail, named after Rachel Carson, the author of Silent Spring and a former resident of the area. It continues north to Wheaton Regional Park, in Greater Silver Spring, which is home to the 50 acre Brookside Gardens.

The 14.5 acre Jessup Blair Park, south of downtown, has a soccer field, tennis courts, basketball courts, and a picnic area. There are similar local parks throughout the residential parts of the community.

2020
As of the 2020 census, 81,015 people lived in Silver Spring. There were 32,114 households; their average annual income was $83,782.

50.9% of the population was female.

33.3% of the population was White (Non-Hispanic), 28% was Black or African American alone (Non-Hispanic), 19.4% of the population was Other (Hispanic), 7.12% of the population was Asian (Non-Hispanic), 6.68% of the population was White (Hispanic), 3.16% was Multiracial (Non-Hispanic), 1.08% was Multiracial (Hispanic), 0.47% was Black or African American (Hispanic), 0.29% was Asian (Hispanic), and 0.19% was American Indian & Alaska Native (Hispanic).

28% of the population identified as Hispanic.

As of 2019, 36.5% of Silver Spring residents (29,800 people) were born outside of the United States, which is higher than the national average of 13.9%. Of these, the most predominant foreign-born people are from El Salvador, Ethiopia, India, and China.

2010
''Note: For the 2010 census, the boundaries of the Silver Spring CDP were changed, reducing the land area by approx. 15%. As a result, the population count for 2010 shows a 6.6% decrease, while the population density increased 11%.''

As of the 2010 census, there were 71,452 residents, 28,603 total households, and 15,684 families residing in the Silver Spring CDP. The population density was 9,021.7 PD/sqmi. There were 30,522 housing units at an average density of 3,853.8 /sqmi. The racial makeup of the community, as defined by the U.S. Census Bureau, for residents who self-identified as being members of "one race" was 45.7% White (7.8% German, 7.0% Irish, 5.7% English), 27.8% Black or African American (5.2% Ethiopian, 1.1% Haitian), 0.6% American Indian and Alaska Native, 7.9% Asian (2.35% Indian, 1.74% Vietnamese, 1.32% Chinese, 0.63% Korean), 0.1% Native Hawaiian and Other Pacific Islander, and 13.2% "Some Other Race" (SOR). 4.8% of the CDP's residents self-identified as being members of two or more races. Hispanic or Latino residents "of any race" comprised 26.3% of the population (12.3% Salvadoran, 3.71% Guatemalan, 2.83% Mexican). Like much of the Washington metropolitan area, Silver Spring is home to many people of Ethiopian ancestry.

There were 28,603 households, out of which 27.1% had children under the age of 18 living with them, 37.6% were married couples living together, 11.9% had a female householder with no husband present, and 45.2% were non-families. 33.6% of all households were made up of individuals living alone, and 16.5% had someone living alone who was 65 years of age or older. The average household size was 2.49 and the average family size was 3.21.

In the census area, the population was spread out, with 21.4% under the age of 18, 9.4% from 18 to 24, 37.1% from 25 to 44, 23.8% from 45 to 64, and 8.4% who were 65 years of age or older. The median age was 33.8 years. For every 100 females, there were 94.9 males, and for every 100 females age 18 and over, there were 92.2 males.

The median income for a household in the census area was US$71986, and the median income for a family was US$84136. Males had a median income of US$46407 versus US$49979 for females. The per capita income for the area was US$32181. 15.0% (±4.9%) of the population and 13.3% (±4.3%) of families were below the poverty line. Twenty-one percent (±9.1%) of those under the age of 18 and 23.6% (±10.6%) of those 65 and older were living below the poverty line.

History
Prior to European settlement, present-day Silver Spring was inhabited by various Indigenous peoples for approximately 10 000 years, including the Piscataway, an Algonquian-speaking people. The Piscataway may have established a few small villages along the banks of Sligo Creek and Rock Creek.

19th century
The Blair, Lee, Jalloh, and Barrie families, three politically active families of the time, are tied to Silver Spring's history. In 1840, Francis Preston Blair, who later helped organize the modern Republican Party, along with his daughter, Elizabeth, discovered a spring flowing with chips of mica believed to be the now-dry spring visible at Acorn Park. Blair was looking for a site for his summer home to escape the summer heat of Washington, D.C. Two years later, Blair completed a 20-room mansion he dubbed "Silver Spring" on a 250 acre country homestead. In 1854, Blair moved to the mansion permanently. The house stood until 1954.

By 1854, Blair's son, Montgomery Blair, who became Postmaster General under Abraham Lincoln and represented Dred Scott before the U.S. Supreme Court, built the Falkland house in the area.

By the end of the decade, Elizabeth Blair married Samuel Phillips Lee, third cousin of future Confederate leader Robert E. Lee, and gave birth to a boy, Francis Preston Blair Lee, who went on to become the first popularly elected Senator in U.S. history.

During the American Civil War, Abraham Lincoln visited the Silver Spring mansion several times, where he relaxed by playing town ball with Francis P. Blair's grandchildren.

In 1864, Confederate States Army General Jubal Early occupied Silver Spring before the Battle of Fort Stevens. After the engagement, fleeing Confederate soldiers razed Montgomery Blair's Falkland residence.

At the time, there was a community called Sligo located at the intersection of the Washington-Brookeville Turnpike and the Washington-Colesville-Ashton Turnpike, now named Georgia Avenue and Colesville Road. Sligo included a tollhouse, a store, a post office, and a few homes. The communities of Woodside, Forest Glen, and Linden were founded after the Civil War. These small towns largely lost their separate identities when a post office was established in Silver Spring in 1899.

By the end of the 19th century, the region began to develop into a town of size and importance. The Baltimore and Ohio Railroad's Metropolitan Branch opened on April 30, 1873, and ran through Silver Spring from Washington, D.C., to Point of Rocks, Maryland.

The first suburban development appeared in 1887 when Selina Wilson divided part of her farm on present-day Colesville Road (U.S. Route 29) and Brookeville Road into five- and ten-acre (20 000 - and 40  000  m2) plots. In 1892, Francis Preston Blair Lee and his wife, Anne Brooke Lee, gave birth to E. Brooke Lee, who is known as the father of modern Silver Spring for his visionary attitude toward developing the region.

20th century
In the early 20th century, E. Brooke Lee and his brother, Blair Lee I, founded the Lee Development Company, whose Colesville Road office building remains a downtown fixture. Dale Drive, a winding roadway, was built to provide vehicular access to much of the family's substantial real estate holdings. Suburban development continued in 1922 when Woodside Development Corporation created Woodside Park, a neighborhood of 1 acre plot home sites built on the former Noyes estate in 1923. In 1924, Washington trolley service on Georgia Avenue (present-day Maryland Route 97) across B&O's Metropolitan Branch was suspended so that an underpass could be built. The underpass was completed two years later, but trolley service never resumed. It would be rebuilt again in 1948 with additional lanes for automobile traffic, opening the areas to the north for readily accessible suburban development.

Takoma-Silver Spring High School, built in 1924, was the first high school for Silver Spring. The community's rapid growth led to the need for a larger school. In 1935, when a new high school building was erected at Wayne Avenue and Sligo Creek Parkway, the school was renamed Montgomery Blair High School. In 1998, the school was moved again, to a new, larger facility at the corner of Colesville Road (U.S. Route 29) and University Boulevard (Maryland Route 193). The former Blair building became a combined middle school and elementary school, housing Silver Spring International Middle School and Sligo Creek Elementary School.

The Silver Spring Shopping Center, built by developer Albert Small and Silver Theatre, designed by theater architect John Eberson, were completed in 1938 at the request of developer William Alexander Julian. The Silver Spring Shopping Center was one of the nation's first retail spaces with a street-front parking lot, defying conventional wisdom that merchandise should be in windows closest to the street so that people could see it. The shopping center was purchased in 1944 by real estate developer Sam Eig, who helped attract large retailers to the city.

Before the 1950s, Silver Spring was known as a sundown town, in part because of influential land owners. The North Washington Real Estate Company designed 63 acres to be white-only, written in its deeds to prevent the sale of land to anyone else. The Fair Housing Act outlawed this practice in 1968, almost two decades after Shelley v. Kramer made racial covenants unenforceable. A 1939 deed for a property owned by Rozier J. Beech in the Sixteenth Street Village subdivision of Silver Spring said, "No negro, or any person or persons of whose blood or extraction or to any person of the semitic race whose blood or origin of racial description will be deemed to include Armenians, Jews, Hebrews, Persians, Syrians, Greeks and Turks, shall use or occupy any building or any lot, except that this covenant shall not prevent occupancy by domestic servants of a different race domiciled with an owner or tenant." In practice, covenants excluding "Semitic races" were primarily used to discriminate against Jews, as Montgomery County did not have significant Armenian, Greek, Iranian, or Turkish populations at the time.

In all, housing in more than 10 square miles of greater Silver Spring was blocked off to Blacks, Jews, Armenians, Persians, Turks, and Greeks, who were considered non-white at the time.

By the 1950s, Silver Spring was the second-busiest retail market between Baltimore and Richmond; major retailers included the Hecht Company, J.C. Penney, and Sears, Roebuck and Company. In 1954, the 1842 Blair mansion "Silver Spring" was razed and replaced with the Blair Station post office. 1960 saw the opening of Wheaton Plaza, later called Westfield Wheaton, a shopping center several miles north of downtown Silver Spring. It captured much of the town's business, and the downtown area began a long period of decline.

On December 19, 1961, a 2 mi segment of the Capital Beltway (I-495) was opened to traffic between Georgia Avenue (MD 97) and University Boulevard East (MD 193). On August 17, 1964, the final segment of the 64 mi Beltway was opened to traffic, and a ribbon-cutting ceremony was held near the New Hampshire Avenue interchange, with a speech by Gov. J. Millard Tawes, who called it a "road of opportunity" for Maryland and the nation.

Washington Metro rail service into Washington, D.C., helped breathe new life into the region starting with the 1978 opening of Silver Spring station. The Metro Red Line followed the right-of-way of the B&O Metropolitan Branch, with the Metro tracks centered between the B&O's eastbound and westbound mains. The Red Line heads south to downtown DC from Silver Spring, running at grade before descending into Union Station. By the mid-1990s, the Red Line continued north from the downtown Silver Spring core, entering a tunnel just past the Silver Spring station and running underground to three more stations: Forest Glen, Wheaton, and Glenmont.

Nevertheless, Silver Spring's downtown continued to decline in the 1980s. The Hecht Company closed its downtown location in 1987 and moved to Wheaton Plaza while forbidding another department store to rent its old spot. City Place, a multi-level mall, was established in the old Hecht Company building in 1992, but it had difficulty attracting quality anchor stores and gained a reputation as a budget mall. In the mid-1990s, developers considered building a mega-mall and entertainment complex called the American Dream, similar to the Mall of America, in downtown Silver Spring, but were unable to secure funding. In the late 1980s and early 1990s, a bright spot was the National Oceanographic and Atmospheric Administration (NOAA)'s consolidationg of its headquarters in four new high-rise office buildings near the Silver Spring Metro station.

A February 16, 1996, train collision on the Silver Spring section of the Metropolitan line left 11 people dead. A MARC commuter train bound for Washington Union Station during the Friday evening rush hour collided with the Amtrak Capitol Limited train and erupted in flames on a snow-swept stretch of track.

The Maryland State Highway Administration started studies of improvements to the Capital Beltway in 1993, and have continued, off and on, examining a number of alternatives since then, including HOV lanes and high-occupancy toll lanes.

21st century
At the beginning of the 21st century, downtown Silver Spring began to see the results of redevelopment. Several city blocks near City Place Mall were rebuilt to accommodate a new outdoor shopping plaza called Downtown Silver Spring. As downtown Silver Spring revived, its 160-year history was celebrated in a 2002 PBS documentary entitled Silver Spring: Story of an American Suburb.

In 2003, Discovery Communications moved its headquarters from nearby Bethesda to a new building in downtown Silver Spring. In 2017, Discovery, Inc. CEO David Zaslav announced that the company was relocating to New York City to operate close to their "ad partners on Madison Avenue," "investors and analysts on Wall Street," and their "creative and production community". ) 2003 also brought the reopening of the Silver Theatre, as AFI Silver, under the auspices of the American Film Institute.

Beginning in 2004, the downtown redevelopment was marketed locally with the "silver sprung" advertising campaign, which declared on buses and in print ads that Silver Spring had "sprung" and was ready for business. In June 2007, The New York Times noted that downtown was "enjoying a renaissance, a result of public involvement and private investment that is turning it into an arts and entertainment center".

In 2005, downtown Silver Spring was awarded the silver medal of the Rudy Bruner Award for Urban Excellence

In 2007, the downtown Silver Spring area gained attention when an amateur photographer was prohibited from taking photographs in what appeared to be a public street. The land, leased to the Peterson Companies, a developer, for $1, was technically private property. The citizens argued that the Downtown Silver Spring development, partially built with public money, was still public property. After a protest on July 4, 2007, Peterson relented and allowed photography on their property under limited conditions. Peterson also claimed that it could revoke these rights at any time. The company further stated that other activities permitted in public spaces, such as organizing protests or distributing campaign literature, were still prohibited. In response, Montgomery County Attorney Leon Rodriguez said that the street in question, Ellsworth Drive, "constitutes a public forum" and that the First Amendment's protection of free speech applies there. In an eight-page letter, Rodriguez wrote, "Although the courts have not definitively resolved the issue of whether the taking, as opposed to the display, of photographs is a protected expressive act, we think it is likely that a court would consider the taking of the photograph to be part of the continuum of action that leads to the display of the photograph and thus also protected by the First Amendment." The incident was part of a trend in the United States regarding the blurring of public and private spaces in developments built with both public and private funds.

In 2008, construction began on the long-planned Intercounty Connector (ICC), which crosses the upper reaches of Silver Spring. The highway's first section opened on February 21, 2011; the entire route was completed by 2012. In July 2010, the Silver Spring Civic Building and Veterans Plaza opened in downtown Silver Spring.

Between 2015 and 2016, the long-struggling City Place Mall was renovated and reopened as Ellsworth Place The old B&O Passenger Station was restored between 2000 and 2002, as recorded in the documentary film Next Stop: Silver Spring.

In May 2019, Peterson announced a $10 million renovation of the Downtown Silver Spring development that will include public art and a new outdoor plaza, featuring green space.

Culture
Downtown Silver Spring hosts several entertainment, musical, and ethnic festivals, the most notable of which are the Silverdocs documentary film festival held each June and hosted by Discovery Communications and the American Film Institute, an annual Thanksgiving Day Parade (Saturday before Thanksgiving) for Montgomery County. The Silver Spring Jazz Festival is the largest annual event, drawing 20 000  people to the free festival held on the second Saturday in September. Featuring local jazz artists and a battle of high school bands, the Silver Spring Jazz Festival has featured Wynton Marsalis, Arturo Sandoval, Sérgio Mendes, Aaron Neville, the Mingus Big Band, the Fred Wesley Group, and other jazz music artists.

The Fillmore is a live entertainment and music venue with a capacity of 2000 people. It opened in 2011 in the former JC Penney building on Colesville Road. The venue joins the American Film Institute and Discovery Communications as cornerstones of the downtown Silver Spring's arts and entertainment district, and has featured performances by artists Prince Royce, Minus the Bear, Tyga, Wale, Schoolboy Q, Migos, and others. In August 2012 R&B singer Reesa Renee launched her album Reelease at the Fillmore.

Downtown Silver Spring is home to the Cultural Arts Center at Montgomery College. The Cultural Arts Center offers a varied set of cultural performances, lectures, films, and conferences. It is a resource for improving cultural literacy, encouraging cross-cultural understanding, and to build bridges between the arts, cultural studies, and other disciplines concerned with the expression of culture.

Dining in Silver Spring is varied, including American, African, Burmese, Ethiopian, Guatemalan, Japanese, Moroccan, Italian, Mexican, Salvadoran, Jamaican, Vietnamese, Lebanese, Thai, Persian, Chinese, Indian, Greek, and fusion restaurants, and national and regional chains.

Silver Spring has several churches, synagogues, temples, and other religious institutions, including the World Headquarters of the Seventh-day Adventist Church. Silver Spring serves as the primary urban area in Montgomery County and its revitalization has ushered in an eclectic mix of people and ideas, evident in the fact that the flagship high school, Montgomery Blair High School, has no majority group with each major racial and ethnic group claiming a significant percentage.

Silver Spring hosts the American Film Institute Silver Theatre and Culture Center, on Colesville Road. The theatre showcases American and foreign films. Gandhi Brigade, a youth development media project, began in Silver Spring out of the Long Branch neighborhood. Docs in Progress, a non-profit media arts center devoted to the promotion of documentary filmmaking is located at the "Documentary House" in downtown Silver Spring. Silver Spring Stage, an all-volunteer community theater, performs in Woodmoor, approximately 3 mi north up Colesville Road from the downtown area. Downtown Silver Spring is also home to the National Oceanic and Atmospheric Administration (NOAA), an agency of the United States Department of Commerce that includes the National Weather Service, the American Nurses Association, and several real estate development, biotechnology, and media and communications companies.

Stevie Nicks of the band Fleetwood Mac has credited Silver Spring as an inspiration for the title of the band's 1977 song "Silver Springs". In a 1998 interview, Nicks said, "I wrote Silver Springs uh, about Lindsey [Buckingham]. And I ~ we were in Maryland somewhere driving under a freeway sign that said Silver Spring, Maryland. And I loved the name. ...Silver Springs sounded like a pretty fabulous place to me. And uh, 'You could be my silver springs...' that's just a whole symbolic thing of what you could have been to me."

Transportation
The major roads in Silver Spring are mostly three- to five-lane highways. The Capital Beltway can be accessed from Georgia Avenue (MD 97), Colesville Road (US 29), and New Hampshire Avenue (MD 650).

The long-planned Intercounty Connector (ICC) (MD-200) toll road opened in three segments between February 2011 and November 2014. ICC interchanges in the Silver Spring area include Georgia Avenue, Layhill Road (MD-182), New Hampshire Avenue, Columbia Pike (US-29) and Briggs Chaney Road.

The multilevel Paul Sarbanes Transit Center in downtown Silver Spring, named in honor of former U.S. Senator Paul Sarbanes from Maryland, is served by the MARC Train on the Brunswick Line, Washington Metro on the Red Line at Silver Spring station, Metrobus, Ride On, the free VanGo, intercity Greyhound bus, and local taxi services. The bus terminal is the busiest in the Washington metropolitan area. This transit facility serves nearly 60 000  passengers daily. The transit center is an expanded version of an older bus, train, and Metro terminal. Begun in October 2008, the expansion, planned to consume $91 million and four years, opened four years late and $50 million over budget on September 20, 2015.

The transit center will also be served by the Purple Line light rail. Under construction by the Maryland Transit Administration (MTA), the line is expected to open in late 2027, and will connect Silver Spring with Bethesda to the west, the University of Maryland, College Park to the east, and the Washington Metro's New Carrollton station to the southeast.

The Washington Metro's Forest Glen station is also located in Silver Spring. MARC Train stops at nearby Kensington station.

Montgomery County Public Schools
Silver Spring is served by Montgomery County Public Schools, a county-wide public school district.

High schools

 * James Hubert Blake High School
 * John F. Kennedy High School
 * Montgomery Blair High School
 * Northwood High School
 * Springbrook High School
 * Wheaton High School

Middle schools

 * Benjamin Banneker Middle School
 * Silver Spring International Middle School
 * Takoma Park Middle School
 * Eastern Middle School
 * White Oak Middle School
 * Briggs Chaney Middle School
 * Argyle Middle School
 * Odessa Shannon Middle School (previously Col. E. Brooke Lee Middle School)
 * Sligo Middle School
 * Francis Scott Key Middle School
 * A. Mario Loiderman Middle School
 * Thornton Friends Middle School
 * Silver Creek Middle School

Prior to 2010, among public high schools in the region, Montgomery Blair High School was the high school located in the census-designated place of Silver Spring. It is nationally recognized for its Communication Arts Program and its Science, Mathematics, and Computer Science Magnet Program, the latter of which perennially produces a large number of finalists and semi-finalists in such academic competitions as the Regeneron Science Talent Search.

Private schools
Notable private schools in Silver Spring include The Siena School, Yeshiva of Greater Washington, the Torah School of Greater Washington, and The Barrie School.

Saint Francis International School St. Camillus Campus, serving kindergarten through 8th grade, is in Silver Spring. It was formerly St. Camillus School, which was operated by sisters of Notre Dame de Namur and opened in 1954. In the middle of the 1960s it had up to 1,200 students. Working-class people were the main clientele. The student population was decreasing by the 1980s as working-class people moved from the area. By the same decade the teachers were mostly lay staff. In the decade of the 2000s the school's financial situation deteriorated. In 2010 the school had 260 students. It merged into Saint Francis International, which opened in 2010; at that time all teachers had to reapply for their jobs. In 2010 Saint Francis International had 435 students at all campuses. In 2014 it had 485 students at all campuses; over 70% the students were of parents born abroad.

Montgomery College
A portion of the Montgomery College, the Takoma Park/Silver Spring campus, is located in the Silver Spring; the rest of the campus located in Takoma Park. The community college is Montgomery County's main institute of higher education; the main campus is in the county seat of Rockville. The campus of the National Labor College is in the White Oak neighborhood in the outer reaches of Silver Spring.

Howard University
Howard University's School of Continuing Education is located in Silver Spring; its main campus in nearby Washington, D.C.

Libraries
Silver Spring is served by many public libraries:

 * Brigadier General Charles E. McGee Library located in downtown Silver Spring.
 * Connie Morrella (formerly Bethesda)
 * Marilyn J. Praisner (formerly Fairland)
 * Wheaton
 * White Oak and Long Branch.

Silver Spring Library started operation in 1931 and is one of the most heavily used in the Montgomery County System. It was relocated in June 2015 to Wayne Avenue and Fenton Street as part of the Downtown Silver Spring redevelopment plan.

Economy
A number of major companies and organizations are based in Silver Spring, including:

 * American Nurses Association, a professional organization
 * CuriosityStream, a streaming media company
 * Food and Drug Administration, a U.S. federal government agency
 * Global Communities, an international development and humanitarian aid nonprofit
 * National Oceanic and Atmospheric Administration, a U.S. federal government agency
 * Urban One, a media company
 * United Therapeutics, a biotechnology company

Sports
The Silver Spring Saints Youth Football Organization has been a mainstay of youth sports in the town since 1951. Located in Silver Spring, the Silver Spring Saints play home games at St. Bernadette's Church near Blair High School. The club was formed when two local Catholic parishes, St. John the Baptist and St. Andrews, merged their football programs to compete in the Capital Beltway League after the CYO (Catholic Youth Organization) for the Archdiocese of Washington D.C. discontinued its youth football program at the end of the 1994 season. The name "Saints" is derived from the merging of the two Catholic parishes. In 2009, the Saints moved from the Capital Beltway League (CBL) to the Mid-Maryland Youth Football & Cheer League (MMYFCL).

Silver Spring is also home to several swim teams, including Parkland, Robin Hood, Calverton, Franklin Knolls, Daleview, Oakview, Forest Knolls, Kemp Mill, Long Branch, Stonegate, Glenwood, Rock Creek, and Northwest Branch, Hillandale, and West Hillandale.

Silver Spring and Takoma Park together host Silver Spring-Takoma Thunderbolts a college wooden-bat baseball team playing in the Cal Ripken, Sr. Collegiate Baseball League. Home games are played at Montgomery Blair Stadium.

The Potomac Athletic Club Rugby team has a youth rugby organization based in Silver Spring. Established in 2005, PAC Youth Rugby has tag rugby for ages 5 to 15, girls and boys and also offer introduction to tackle rugby for U13 and U15 players. In addition to introducing numerous young athletes to the sport of rugby, PAC has also won Maryland state championships across the age groups.

Media
Silver Spring is served by Washington metropolitan area media, including two daily newspapers, The Washington Post and The Washington Times, and several online outlets. The Gazette and the Montgomery County Sentinel were available historically until their closures in 2015 and 2020, respectively.

The Washington Hispanic has its offices in Silver Spring.

Companies headquartered in Silver Spring include Urban One. After relocating to New York City in 2018, Discovery Inc. sold its former Silver Spring headquarters to Foulger-Pratt and Cerberus Capital Management, and leased a smaller space at nearby 8403 Colesville Road.

Notable people

 * Joe Alexander, (b. 1986), American-Israeli basketball player in the Israel Basketball Premier League
 * Brady Anderson, (b. 1964), baseball player
 * Akil Baddoo, (b. 1998), baseball player for the Detroit Tigers
 * Jonathan Banks, (b. 1947), actor
 * Alex Bazzie, (b. 1990), football player
 * Carl Bernstein, (b. 1944), journalist, writer
 * Keter Betts, (1928–2005), musician
 * Lewis Black, (b. 1948), comedian
 * Brandon Broady, (b. 1986), comedian, television host
 * Laphonza Butler, U.S. senator
 * Bill Callahan, (b. 1966), musician
 * Rachel Carson, (1907–1964), author of Silent Spring
 * Crystal Chappell, (b. 1965), actress
 * Dave Chappelle, (b. 1973), comedian
 * Connie Chung, (b. 1946), news presenter
 * Gaelan Connel, (b. 1989), actor, musician
 * Chuck Davidson, (b. 1961), rabbi
 * Tommy Davidson, (b. 1963), comedian, actor
 * Marc Davis, (b. 1990), NASCAR driver
 * Dominique Dawes, (b. 1976), gymnast, 4-time Olympic medalist
 * Cara DeLizia, (b. 1984), actress
 * Matt Drudge, (b. 1966), internet news editor
 * Michael Ealy, (b. 1973), actor
 * Wayne Federman, (b. 1959), comedian, actor, writer
 * Charles Fefferman, (b. 1949), mathematician
 * David Feldberg, (b. 1977), professional disc golfer
 * Martin Felsen, (b. 1968), architect
 * John Meredith Ford (1923–1995), Guyanese politician, died in Silver Spring
 * Steve Francis, former basketball player
 * Jason Freeny, (b. 1970), sculptor, toy designer
 * Kimmy Gatewood, actress, writer and singer
 * Emily Gould, (b. 1981), author
 * Jerian Grant, (b. 1992), basketball player for the Washington Wizards
 * Josh Hart, (b. 1995) basketball player for the New York Knicks; first-round selection in 2017 NBA draft
 * Goldie Hawn, (b. 1945), actress, dancer, producer, and singer
 * Keith Howland, (b. 1964), musician (Chicago)
 * Frank Jackson (b. 1998), NBA player
 * Rian Johnson, (b. 1973), film director
 * Jesse Mockrin, (b. 1981), artist
 * Amir Mohamed el Khalifa, better known by his stage name Oddisee, is an American rapper
 * Humayun Khan, (1976 – 2004) U.S. Army Officer of Pakistani descent and a Muslim, posthumous recipient of the Purple Heart and the Bronze Star Medal.
 * Rick Leventhal, (b. 1960), journalist
 * Elliot Levine, (b. 1963), musician (Heatwave)
 * Dov Lipman, (b. 1971), member of the Knesset.
 * Matt Maloney, (b. 1971), former basketball player
 * Michelle M. Marciniak, (b. 1973), former WNBA professional basketball player and collegiate coach
 * Roger Mason Jr., (b. 1980), former basketball player
 * Joey Mbu, (b. 1993), football player
 * Victor Oladipo, (b. 1992), basketball player for the Houston Rockets
 * George Pelecanos, (b. 1957), author
 * Al Quie, (b. 1923), former Governor of Minnesota (1979–1983)
 * Gretchen Quie, (1927–2015), artist and former First Lady of Minnesota (1979–1983)
 * J. Robbins, (b. 1967), musician (Jawbox, Office of Future Plans)
 * Nora Roberts, (b. 1950), novelist
 * Daniel Snyder, (b. 1964), businessperson and former owner of the Washington Commanders
 * Harold Solomon (b. 1952), tennis player ranked No. 5 in the world
 * Norman Solomon, (b. 1951), journalist, political candidate
 * Ben Stein, (b. 1944), commentator, humorist, actor
 * Rebecca Sugar, (b. ca. 1987), artist, composer, and director
 * Daryush Valizadeh, (b. 1979), neomasculinity writer
 * Thalia Zedek, (b. 1961), musician (Live Skull, Come)

Documentary films

 * Silver Spring: Story of an American Suburb
 * Next Stop: Silver Spring
 * Silver Spring Stories

title: Silver Spring, Maryland


text:
Moulin Rouge

Moulin Rouge (, ; lit. '"Red Mill"') is a cabaret in Paris, on Boulevard de Clichy, at Place Blanche, the intersection of, and terminus of Rue Blanche.

In 1889, the Moulin Rouge was co-founded by Charles Zidler and Joseph Oller, who also owned the Paris Olympia. The original venue was destroyed by fire in 1915. Moulin Rouge is southwest of Montmartre, in the Paris district of Pigalle on Boulevard de Clichy in the 18th arrondissement, and has a landmark red windmill on its roof. The closest métro station is Blanche.

Moulin Rouge is best known as the birthplace of the modern form of the can-can dance. Originally introduced as a seductive dance by the courtesans who operated from the site, the can-can dance revue evolved into a form of entertainment of its own and led to the introduction of cabarets across Europe. Today, the Moulin Rouge is a tourist attraction, offering predominantly musical dance entertainment for visitors from around the world. The club's decor still contains much of the romance of fin de siècle France.

Background
The Belle Époque, a period characterized by peace, optimism, and industrial progress, witnessed a notable cultural flourishing exemplified by the opening of the Moulin Rouge. The Expositions Universelles of 1889 and 1900 are symbols of this period.

In 1889, the construction of the Eiffel Tower symbolized progress, coinciding with the culturally innovative cabaret scene. The artistic movement of Japonism, influenced by the Orient, thrived during this period, with Henri de Toulouse-Lautrec emerging as a prominent figure. Montmartre, situated within the expanding city of Paris, maintained its bohemian village atmosphere, where festivities and artists embraced values of pleasure and beauty.

Creation and early success
On 6 October 1889, the Moulin Rouge opened as the Jardin de Paris, an outdoor garden café-concert, at the foot of the Montmartre hill. Its creator Joseph Oller and his Manager Charles Zidler were formidable businessmen who understood the public's tastes. The aim was to attract wealthy individuals to experience the ambiance of the fashionable district of Montmartre, which was perceived as a form of slumming. The elaborate setting, featuring a garden adorned with a large elephant, provided an environment where individuals from various social strata could interact. This included workers, local residents, artists, the middle class, businessmen, stylish women, and tourists passing through Paris. Nicknamed "The First Palace of Women" by Oller and Zidler, the cabaret swiftly garnered significant acclaim. Key factors contributing to its success included:
 * Revolutionary auditorium architecture enabling rapid changes of décor and fostering social interaction among all patrons.
 * Champagne evenings characterized by lively entertainment and dancing, featuring regularly changing amusing acts like Le Pétomane.
 * A new dance, inspired by the quadrille and gaining popularity, known as the Can-can. Dancers performed this energetic dance to a lively rhythm while wearing provocative costumes.
 * Prominent dancers from the era included figures such as la Goulue, Jane Avril, la Môme Fromage, Grille d'Egout, Nini Pattes en l'Air, Yvette Guilbert, Valentin le désossé, and the clown Cha-U-Kao.
 * A favored venue among artists, including Toulouse-Lautrec, whose posters and paintings contributed to the rapid and international renown of the Moulin Rouge.

Greatest moments
During its early years, the Moulin Rouge featured extravagant shows inspired by the circus, along with attractions that gained widespread fame, such as Pétomane. Concert-dances were organized daily at 10 pm. Between 1886 and 1910, the comic duo Footit and Chocolat, comprising a white authoritarian clown and a black long-suffering Auguste, gained popularity and were frequently featured on Moulin Rouge posters.

On 19 April 1890, the first revue, "Circassiens et Circassiennes," debuted. On 26 October 1890, during a private visit to Paris, the Prince of Wales, later Edward VII, reserved a table to witness a quadrille at the Moulin Rouge, where La Goulue famously greeted him with the exclamation, "Hey, Wales, the champagne's on you!" In 1891, Toulouse-Lautrec created his first poster for the Moulin Rouge, featuring La Goulue.

In 1893, the "Bal des Quat'z'Arts" sparked scandal with its procession featuring a nude Cleopatra surrounded by young naked women. On 12 November 1897, the Moulin Rouge closed for the first time to mourn the passing of its manager and co-founder, Charles Zidler. Yvette Guilbert paid homage to him, saying, "You have the knack of creating popular pleasure, in the finest sense of the word, of entertaining crowds with subtlety, according to the status of those to be entertained."

In 1900, the Universal Exhibition attracted visitors from around the world to the Moulin Rouge, solidifying Paris's reputation as a city of decadent pleasure. This led to the establishment of imitation "Moulin Rouges" and "Montmartres" in many other countries.

Operetta and grand shows
In January 1903, the Moulin Rouge underwent renovation and improvement under the direction of Édouard Niermans, a prominent architect of the Belle Époque era, amongst other works he designed the brasserie Mollard, the Casino de Paris, the Folies Bergère in Paris, the Palace Hôtel in Ostend in Belgium, the rebuilding of the Hôtel du Palais in Biarritz, and the creation of the Hotel Negresco on the Promenade des Anglais in Nice. This included the addition of aperitif concerts, attracting the fashionable elite for dining and entertainment in a luxurious setting.

Until the outbreak of the First World War, the Moulin Rouge became renowned for its operetta performances. Successful shows during this period included Voluptata, La Feuille de Vigne, Le Rêve d'Egypte, Tais-toi tu m'affoles, among others, each with evocative titles.

On 3 January 1907, during the performance of Le Rêve d'Egypte, Colette exchanged scandalous kisses that revealed her connection to the Duchess of Morny, leading to the show being banned.

Mistinguett made her debut at the Moulin Rouge on 29 July 1907 in the Revue de la Femme, showcasing her undeniable talent. She quickly rose to fame, achieving immense success the following year with Max Dearly in La Valse chaloupée. Born into poverty, Mistinguett's sharp wit and determination propelled her to become a successful businesswoman, touring extensively across Europe and the United States.

On 9 April 1910, a former lady-in-waiting to Empress Eugénie attended a showing of the Revue Amoureuse at the Moulin Rouge and was so captivated by the faithful recreation of a ceremony for the return of troops from Italy that she exclaimed, "Long Live the Empress!"

Tragically, on 27 February 1915, the Moulin Rouge was destroyed by fire during building works, resulting in a nine-year closure. In 1925, the rebuilt Moulin Rouge reopened its doors to the public.

Mistinguett years
Following World War I, Francis Salabert assumed management of the Moulin Rouge. As a businessman rather than a showman, he entrusted Jacques-Charles, a prominent impresario, with revitalizing the cabaret. The Moulin Rouge experienced a resurgence with the performances of stars such as Mistinguett, Jeanne Aubert, and Maurice Chevalier, as well as the introduction of American revues featuring the Hoffmann Girls.

In 1923, composer and conductor Raphaël Beretta proposed a reconstruction of the Moulin Rouge's music hall on a larger scale. The iconic mill structure, supported by a central facade adorned with oval dormers, was designed by Gesmar, a 20-year-old set designer whose work became synonymous with the venue.

Jacques-Charles and Mistinguett collaborated on several acclaimed revues, including:

1925: Revue Mistinguett

1926: Ça c'est Paris

1928: Paris qui tourne

During a 1927 performance, an incident occurred when female dancers emerged from multi-tiered artificial cakes covered in real frosting. The slippery cake cream on their high heels caused them to repeatedly slip and fall on stage, resulting in disruptions to the show.

Mistinguett's tenure at the Moulin Rouge produced enduring songs such as "Valencia," "Ça c'est Paris" (both by Jose Padilla), "Il m'a vue nue," "On m' suit," and "La Java de Doudoune," the latter performed with Jean Gabin.

After Mistinguett
In 1929, Mistinguett retired from the stage, leading to the transformation of the Moulin Rouge's ballroom into an ultra-modern Night Club.

From June to August 1929, the revue Lew Leslie's Blackbirds, featuring jazz singer and Broadway star Adelaide Hall, along with a troop of a hundred black artists accompanied by the Jazz Plantation Orchestra, became the hit of the season at the Moulin Rouge.

In 1937, the Cotton Club, renowned in New York, was showcased at the Moulin Rouge, alongside performances by Ray Ventura and his Collegians.

During the Second World War (1939–1945), the Moulin Rouge was highlighted in the German Occupation Guide as a must-visit attraction in Paris. Its stage shows continued for the occupation troops and were mentioned in autobiographies of German officers such as Ernst Jünger and Gerhard Heller. The Germans facilitated "recreational visits" in Paris for their troops, promoting the motto "Jeder einmal in Paris" (everyone once in Paris). The widespread prostitution during the occupation eventually led to the implementation of the Loi Marthe Richard in 1946, which closed bordellos and reduced stage shows to dancing events.

In 1944, shortly after the liberation of Paris, Edith Piaf, who had performed frequently at social gatherings for German forces during the war, returned to the stage at the Moulin Rouge. She was accompanied by Yves Montand, a newcomer chosen to perform with her.

Renewal
On June 22, 1951, Georges France, also known as Jo France, founder of the Balajo in Paris, acquired the Moulin Rouge and initiated extensive renovation efforts. Architects Pierre Devinoy, Bernard de La Tour d’Auvergne, and Marion Tournon-Branly were tasked with enhancing and outfitting the new auditorium. The envisioned décor by Jo France, largely executed by Henri Mahé, a prominent designer of the era, remains intact to this day.

The return of evening dances, acts, and the iconic French cancan marked a revival at the Moulin Rouge. On May 19, 1953, the 25th "Bal des Petits Lits Blancs," organized by novelist Guy des Cars, attracted notable figures such as French President Vincent Auriol and featured Bing Crosby's European stage debut. Between 1951 and 1960, the stage saw performances by renowned artists including Luis Mariano, Charles Trénet, and Josephine Baker.

In 1955, Jo France transferred ownership to brothers Joseph and Louis Clérico, proprietors of Le Lido, with Jean Bauchet assuming the managerial role. The tradition of the French cancan continued, choreographed by Ruggero Angeletti. Doris Haug established the "Doris's Girls" troop in 1957, initially comprising four girls and later expanding to sixty.

Transformations in 1959 included renovations to the Moulin Rouge's kitchens, while the introduction of The Revue Japonaise in 1960 showcased Japanese artists and popularized Kabuki in Montmartre. In 1962, Jacki Clérico, son of Joseph Clérico, assumed leadership, ushering in an era of expansion with the enlargement of the auditorium, installation of a giant aquarium, and the introduction of the first aquatic ballet. The Revue Cancan, devised by Doris Haug and Ruggero Angeletti, premiered the same year.

Since 1963, following the success of the Frou-Frou revue, Jacki Clérico adopted a tradition of naming revues with titles beginning with the letter F. Throughout these productions, the famed French cancan remained a staple feature.
 * 1963–1965 : Frou-Frou
 * 1965–1967 : Frisson
 * 1967–1970 : Fascination
 * 1970–1973 : Fantastic
 * 1973–1976 : Festival
 * 1976–1978 : Follement
 * 1978–1983 : Frénésie
 * 1983–1988 : Femmes, femmes, femmes
 * 1988–1999 : Formidable
 * Since 1999: Féerie

On September 7, 1979, the Moulin Rouge marked its 90th anniversary, reaffirming its status as a prominent fixture in Parisian nightlife. The celebration featured an array of stars, including Ginger Rogers, Thierry Le Luron, Dalida, and Charles Aznavour, among others. Notable events followed, including a special presentation of the show to Her Majesty Queen Elizabeth II on November 23, 1981. The venue hosted renowned performers such as Liza Minnelli in February 1982, followed by gala performances with Dean Martin in July 1984 and Frank Sinatra in September 1984. A milestone occurred on December 1, 1986, when world-renowned dancer Mikhail Baryshnikov premiered an original ballet by Maurice Béjart at the Moulin Rouge.

In February 1988, despite the original building's destruction in 1915, the Moulin Rouge celebrated its centenary with the premiere of the revue "Formidable," a prestigious event attended by Prince Edward. Subsequent events included performances in London and gala celebrations featuring an array of luminaries, including Charles Aznavour, Ella Fitzgerald, and Jerry Lewis. Over the years, the Moulin Rouge continued to host charitable events, such as the Cartier gala in support of the Artists' Foundation against AIDS in 1994, and the Lancôme gala in 1995. The centenary revue "Formidable" concluded in November 1999, paving the way for the debut of the new revue "Féerie" in December 1999.

In 2008, soloist dancer Aleksandar Josipović served as master of ceremonies at the 53rd Eurovision Song Contest. The venue's global reach extended further in February 2009 when it was showcased as part of the Year of France in Brazil and the Rio Carnival on Copacabana Beach. However, on January 13, 2013, Moulin Rouge owner Jacki Clérico passed away, followed by the death of Doris Haug, founder of the Doris's Girls, on August 10, 2014. Despite these losses, the Moulin Rouge celebrated its 125th anniversary on October 6, 2014. On April 25, 2024, the cabaret's windmill blades collapsed onto the street, resulting in damage to the facade. No injuries were reported. The windmill was restored on 5 July that year, in time for the Olympic torch relay that will pass through the area on 15 July.

Documentaries

 * Quadrille dansé par les étoiles du Moulin-Rouge 1,2&3 (1899–1902), France – produced by Pathé (3 episodes of 20 min)
 * An Evening at the Moulin Rouge (1981), Réalisé par David Niles, produced by HBO (length : 60 min)
 * Les Dessous du Moulin Rouge (2000), Réalisé par Nils Tavernier, produced by Little Bear (length : 52 min)
 * Coulisses d'une revue, le Moulin Rouge (2001), directed by par Philippe Pouchain and Yves Riou (length : 60 min)
 * Moulin Rouge Forever (2002), directed by Philippe Pouchain and Yves Riou (length: 55 min)
 * Moulin Rouge : la restauration and Une vie de passion au Moulin Rouge. Two documentaries available with the Moulin Rouge movie of John Huston.
 * Au cœur du Moulin Rouge (At the heart of Moulin Rouge) (2012), Directed by Marie Vabre, produced by 3e Œil Productions (90 min).

Illustrated books

 * The Moulin Rouge (1989), by Jacques Pessis and Jacques Crépineau – Publisher: St Martins
 * The Moulin Rouge (2002), by Jacques Pessis and Jacques Crépineau – Publisher: Le Cherche-Midi
 * Moulin Rouge, Paris (2002), by Christophe Mirambeau – Publisher: Assouline
 * Flipbook Moulin Rouge Paris France 23h18, Paris (2003), by Jean-Luc Planche – Publisher: Youpeka

About Moulin Rouge and its characters

 * Pierre La Mure Moulin Rouge (1950), a novel based on the life of Henri de Toulouse-Lautrec, Random House
 * Jose Shercliff Jane Avril of the Moulin Rouge (1954), Macrae Smith Co
 * Jean Nohain and François Caradec Le Pétomane 1857–1945 a tribute to the unique act which shook and shattered the Moulin-Rouge (1967), Souvenir Press
 * Robert Burleigh Toulouse-Lautrec : The Moulin Rouge And The City Of Light, (2003), Harry N. Abrams
 * Robert Burleigh Toulouse-Lautrec : The Moulin Rouge And The City Of Light, (2003), Harry N. Abrams

Enterprises
The Moulin Rouge in Paris was a source of inspiration for:
 * Moulin Rouge Hotel in Las Vegas, Nevada
 * The nude revues at the Windmill Theatre, created by Laura Henderson and Vivian Van Damm
 * The Moulin Rouge restaurant in Park Street, Kolkata is inspired by this cabaret along with the symbolic windmill.

Film

 * Moulin Rouge Dancers 1&2 (1898) – United States – silent film about the Moulin Rouge
 * Queen of the Moulin Rouge (1922), directed by Ray C. Smallwood and Peter Milne – United States – silent film about the Moulin Rouge
 * Le Fantôme du Moulin Rouge (1925), directed by René Clair – with Sandra Milovanoff and Georges Vaultier
 * Moulin Rouge (1928), directed by Ewald André Dupont – With Olga Chekhova, Eve Gray and Jean Bradin
 * Moulin Rouge also titled L'étoile du Moulin Rouge (1934), directed by Sidney Lanfield – with Constance Bennett – United States
 * La Chaste Suzanne (1937/1938), directed by André Berthomieu – with Raimu and Henri Garat
 * La P'tite femme du Moulin Rouge (1945), directed by Benito Perojo – with Alberto Bello, Héctor Calcaño, Homero Cárpena, and Tilda Thamar
 * A Night at the Moulin Rouge (1951) is a film (also circulated under the title Ding Dong!) of burlesque acts of the Moulin Rouge club in Oakland, California
 * Moulin Rouge (1952), directed by John Huston- with José Ferrer, Suzanne Flon and Zsa Zsa Gabor
 * French Cancan (1955), directed by Jean Renoir – with Jean Gabin, Françoise Arnoul, María Félix, Jean-Roger Caussimon, Gianni Esposito, Philippe Clay, and Michel Piccoli
 * A Night at the Moulin Rouge (1957), directed by Jean-Claude Roy – with Tilda Thamar, Noël Roquevert, Armand Bernard and Jean Tissier
 * La Chaste Suzanne (1963), directed by Luis César Amadori – with Armand Mestral, Noël Roquevert and Frédéric Duvallès – Spain/France
 * Moulin Rouge! (2001), directed by Baz Luhrmann, with Ewan McGregor, Nicole Kidman, John Leguizamo, Jim Broadbent, and Richard Roxburgh
 * Midnight in Paris (2011), directed by Woody Allen, with Owen Wilson, Marion Cotillard, Rachel McAdams, Tom Hiddleston, Corey Stoll, Kathy Bates, and Adrien Brody - Spain, US

Music

 * The music video for the "Lady Marmalade" cover act by Christina Aguilera, Pink, Lil' Kim, and Mýa was filmed on a replica set of the Moulin Rouge
 * Prince and his concert film Sign o' the Times (1987) featured the Moulin Rouge as part of his stage venue and props
 * The second music video for The Killers' song "Mr. Brightside" was set in the Moulin Rouge

Stage adaptations

 * The 2018 musical Moulin Rouge! is an adaptation of the 2001 Baz Luhrmann film.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Moulin Rouge


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Probability density function

In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would be equal to that sample. Probability density is the  probability per unit length,  in other words, while the absolute likelihood for a continuous random variable to take on any particular value is 0 (since there is an infinite set of possible values to begin with), the value of the PDF at two different samples can be used to infer, in any particular draw of the random variable, how much more likely it is that the random variable would be close to one sample compared to the other sample.

More precisely, the PDF is used to specify the probability of the random variable falling within a particular range of values, as opposed to taking on any one value. This probability is given by the integral of this variable's PDF over that range—that is, it is given by the area under the density function but above the horizontal axis and between the lowest and greatest values of the range. The probability density function is nonnegative everywhere, and the area under the entire curve is equal to 1.

The terms probability distribution function and probability function have also sometimes been used to denote the probability density function. However, this use is not standard among probabilists and statisticians. In other sources, "probability distribution function" may be used when the probability distribution is defined as a function over general sets of values or it may refer to the cumulative distribution function, or it may be a probability mass function (PMF) rather than the density. "Density function" itself is also used for the probability mass function, leading to further confusion. In general though, the PMF is used in the context of discrete random variables (random variables that take values on a countable set), while the PDF is used in the context of continuous random variables.

Example

Suppose bacteria of a certain species typically live 20 to 30 hours. The probability that a bacterium lives 5 hours is equal to zero. A lot of bacteria live for approximately 5 hours, but there is no chance that any given bacterium dies at exactly 5.00... hours. However, the probability that the bacterium dies between 5 hours and 5.01 hours is quantifiable. Suppose the answer is 0.02 (i.e., 2%). Then, the probability that the bacterium dies between 5 hours and 5.001 hours should be about 0.087, since this time interval is one-tenth as long as the previous. The probability that the bacterium dies between 5 hours and 5.0001 hours should be about 0.0087, and so on.

In this example, the ratio (probability of living during an interval) / (duration of the interval) is approximately constant, and equal to 2 per hour (or 2 hour−1). For example, there is 0.02 probability of dying in the 0.01-hour interval between 5 and 5.01 hours, and (0.02 probability / 0.01 hours) = 2 hour−1. This quantity 2 hour−1 is called the probability density for dying at around 5 hours. Therefore, the probability that the bacterium dies at 5 hours can be written as (2 hour−1) dt. This is the probability that the bacterium dies within an infinitesimal window of time around 5 hours, where dt is the duration of this window. For example, the probability that it lives longer than 5 hours, but shorter than (5 hours + 1 nanosecond), is (2 hour−1)×(1 nanosecond) ≈ $0$ (using the unit conversion $3,600,000,000,000$ nanoseconds = 1 hour).

There is a probability density function f with f(5 hours) = 2 hour−1. The integral of f over any window of time (not only infinitesimal windows but also large windows) is the probability that the bacterium dies in that window.

Absolutely continuous univariate distributions
A probability density function is most commonly associated with absolutely continuous univariate distributions. A random variable $$X$$ has density $$f_X$$, where $$f_X$$ is a non-negative Lebesgue-integrable function, if: $$ \Pr [a \le X \le b] = \int_a^b f_X(x) \, dx .$$

Hence, if $$F_X$$ is the cumulative distribution function of $$X$$, then: $$F_X(x) = \int_{-\infty}^x f_X(u) \, du ,$$ and (if $$f_X$$ is continuous at $$x$$) $$ f_X(x) = \frac{d}{dx} F_X(x) .$$

Intuitively, one can think of $$f_X(x) \, dx$$ as being the probability of $$X$$ falling within the infinitesimal interval $$[x,x+dx]$$.

Formal definition
(This definition may be extended to any probability distribution using the measure-theoretic definition of probability.)

A random variable $$X$$ with values in a measurable space $$(\mathcal{X}, \mathcal{A})$$ (usually $$\mathbb{R}^n$$ with the Borel sets as measurable subsets) has as probability distribution the measure X∗P on $$(\mathcal{X}, \mathcal{A})$$: the density of $$X$$ with respect to a reference measure $$\mu$$ on $$(\mathcal{X}, \mathcal{A})$$ is the Radon–Nikodym derivative: $$f = \frac{dX_*P}{d\mu} .$$

That is, f is any measurable function with the property that: $$\Pr [X \in A ] = \int_{X^{-1} A} \, dP = \int_A f \, d\mu $$ for any measurable set $$A \in \mathcal{A}.$$

Discussion
In the continuous univariate case above, the reference measure is the Lebesgue measure. The probability mass function of a discrete random variable is the density with respect to the counting measure over the sample space (usually the set of integers, or some subset thereof).

It is not possible to define a density with reference to an arbitrary measure (e.g. one can not choose the counting measure as a reference for a continuous random variable). Furthermore, when it does exist, the density is almost unique, meaning that any two such densities coincide almost everywhere.

Further details
Unlike a probability, a probability density function can take on values greater than one; for example, the continuous uniform distribution on the interval $[0, 1/2]$ has probability density $N(0, σ^{2})$ for $f(x) = 2$ and $0 ≤ x ≤ 1/2$ elsewhere.

The standard normal distribution has probability density $$f(x) = \frac{1}{\sqrt{2\pi}}\, e^{-x^2/2}.$$

If a random variable $f(x) = 0$ is given and its distribution admits a probability density function $X$, then the expected value of $f$ (if the expected value exists) can be calculated as $$\operatorname{E}[X] = \int_{-\infty}^\infty x\,f(x)\,dx.$$

Not every probability distribution has a density function: the distributions of discrete random variables do not; nor does the Cantor distribution, even though it has no discrete component, i.e., does not assign positive probability to any individual point.

A distribution has a density function if and only if its cumulative distribution function $X$ is absolutely continuous. In this case: $F(x)$ is almost everywhere differentiable, and its derivative can be used as probability density: $$\frac{d}{dx}F(x) = f(x).$$

If a probability distribution admits a density, then the probability of every one-point set $F$ is zero; the same holds for finite and countable sets.

Two probability densities ${a}$ and $f$ represent the same probability distribution precisely if they differ only on a set of Lebesgue measure zero.

In the field of statistical physics, a non-formal reformulation of the relation above between the derivative of the cumulative distribution function and the probability density function is generally used as the definition of the probability density function. This alternate definition is the following:

If $g$ is an infinitely small number, the probability that $dt$ is included within the interval $(t, t + dt)$ is equal to $X$, or: $$\Pr(t<X<t+dt) = f(t)\,dt.$$

Link between discrete and continuous distributions
It is possible to represent certain discrete random variables as well as random variables involving both a continuous and a discrete part with a generalized probability density function using the Dirac delta function. (This is not possible with a probability density function in the sense defined above, it may be done with a distribution.) For example, consider a binary discrete random variable having the Rademacher distribution—that is, taking −1 or 1 for values, with probability 1⁄2 each. The density of probability associated with this variable is: $$f(t) = \frac{1}{2} (\delta(t+1)+\delta(t-1)).$$

More generally, if a discrete variable can take $n$ different values among real numbers, then the associated probability density function is: $$f(t) = \sum_{i=1}^n p_i\, \delta(t-x_i),$$ where $$x_1, \ldots, x_n$$ are the discrete values accessible to the variable and $$p_1, \ldots, p_n$$ are the probabilities associated with these values.

This substantially unifies the treatment of discrete and continuous probability distributions. The above expression allows for determining statistical characteristics of such a discrete variable (such as the mean, variance, and kurtosis), starting from the formulas given for a continuous distribution of the probability.

Families of densities
It is common for probability density functions (and probability mass functions) to be parametrized—that is, to be characterized by unspecified parameters. For example, the normal distribution is parametrized in terms of the mean and the variance, denoted by $$\mu$$ and $$\sigma^2$$ respectively, giving the family of densities $$  f(x;\mu,\sigma^2) = \frac{1}{\sigma\sqrt{2\pi}} e^{ -\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2 }. $$ Different values of the parameters describe different distributions of different random variables on the same sample space (the same set of all possible values of the variable); this sample space is the domain of the family of random variables that this family of distributions describes. A given set of parameters describes a single distribution within the family sharing the functional form of the density. From the perspective of a given distribution, the parameters are constants, and terms in a density function that contain only parameters, but not variables, are part of the normalization factor of a distribution (the multiplicative factor that ensures that the area under the density—the probability of something in the domain occurring— equals 1). This normalization factor is outside the kernel of the distribution.

Since the parameters are constants, reparametrizing a density in terms of different parameters to give a characterization of a different random variable in the family, means simply substituting the new parameter values into the formula in place of the old ones.

Densities associated with multiple variables
For continuous random variables $f(t) dt$, it is also possible to define a probability density function associated to the set as a whole, often called joint probability density function. This density function is defined as a function of the $n$ variables, such that, for any domain $D$ in the $n$-dimensional space of the values of the variables $X_{1}, ..., X_{n}$, the probability that a realisation of the set variables falls inside the domain $D$ is $$\Pr \left( X_1,\ldots,X_n \isin D \right) = \int_D f_{X_1,\ldots,X_n}(x_1,\ldots,x_n)\,dx_1 \cdots dx_n.$$

If $X_{1}, ..., X_{n}$ is the cumulative distribution function of the vector $F(x_{1}, ..., x_{n}) = Pr(X_{1} ≤ x_{1}, ..., X_{n} ≤ x_{n})$, then the joint probability density function can be computed as a partial derivative $$ f(x) = \left.\frac{\partial^n F}{\partial x_1 \cdots \partial x_n} \right|_x $$

Marginal densities
For $(X_{1}, ..., X_{n})$, let $i = 1, 2, ..., n$ be the probability density function associated with variable $f_{X_{i}}(x_{i})|undefined$ alone. This is called the marginal density function, and can be deduced from the probability density associated with the random variables $X_{i}$ by integrating over all values of the other $X_{1}, ..., X_{n}$ variables: $$f_{X_i}(x_i) = \int f(x_1,\ldots,x_n)\, dx_1 \cdots dx_{i-1}\,dx_{i+1}\cdots dx_n .$$

Independence
Continuous random variables $n − 1$ admitting a joint density are all independent from each other if and only if $$f_{X_1,\ldots,X_n}(x_1,\ldots,x_n) = f_{X_1}(x_1)\cdots f_{X_n}(x_n).$$

Corollary
If the joint probability density function of a vector of $n$ random variables can be factored into a product of $n$ functions of one variable $$f_{X_1,\ldots,X_n}(x_1,\ldots,x_n) = f_1(x_1)\cdots f_n(x_n),$$ (where each $X_{1}, ..., X_{n}$ is not necessarily a density) then the $n$ variables in the set are all independent from each other, and the marginal probability density function of each of them is given by $$f_{X_i}(x_i) = \frac{f_i(x_i)}{\int f_i(x)\,dx}.$$

Example
This elementary example illustrates the above definition of multidimensional probability density functions in the simple case of a function of a set of two variables. Let us call $$\vec R$$ a 2-dimensional random vector of coordinates $f_{i}$: the probability to obtain $$\vec R$$ in the quarter plane of positive $(X, Y)$ and $x$ is $$\Pr \left( X > 0, Y > 0 \right) = \int_0^\infty \int_0^\infty f_{X,Y}(x,y)\,dx\,dy.$$

Function of random variables and change of variables in the probability density function
If the probability density function of a random variable (or vector) $y$ is given as $X$, it is possible (but often not necessary; see below) to calculate the probability density function of some variable $f_{X}(x)$. This is also called a "change of variable" and is in practice used to generate a random variable of arbitrary shape $Y = g(X)$ using a known (for instance, uniform) random number generator.

It is tempting to think that in order to find the expected value $f_{g(X)} = f_{Y}$, one must first find the probability density $E(g(X))$ of the new random variable $f_{g(X)}$. However, rather than computing $$\operatorname E\big(g(X)\big) = \int_{-\infty}^\infty y f_{g(X)}(y)\,dy, $$ one may find instead $$\operatorname E\big(g(X)\big) = \int_{-\infty}^\infty g(x) f_X(x)\,dx.$$

The values of the two integrals are the same in all cases in which both $Y = g(X)$ and $X$ actually have probability density functions. It is not necessary that $g(X)$ be a one-to-one function. In some cases the latter integral is computed much more easily than the former. See Law of the unconscious statistician.

Scalar to scalar
Let $$ g: \Reals \to \Reals$$ be a monotonic function, then the resulting density function is $$f_Y(y) = f_X\big(g^{-1}(y)\big) \left| \frac{d}{dy} \big(g^{-1}(y)\big) \right|.$$

Here $g$ denotes the inverse function.

This follows from the fact that the probability contained in a differential area must be invariant under change of variables. That is, $$\left| f_Y(y)\, dy \right| = \left| f_X(x)\, dx \right|,$$ or $$f_Y(y) = \left| \frac{dx}{dy} \right| f_X(x) = \left| \frac{d}{dy} (x) \right| f_X(x) = \left| \frac{d}{dy} \big(g^{-1}(y)\big) \right| f_X\big(g^{-1}(y)\big) = {\left|\left(g^{-1}\right)'(y)\right|} \cdot f_X\big(g^{-1}(y)\big) .$$

For functions that are not monotonic, the probability density function for $y$ is $$\sum_{k=1}^{n(y)} \left| \frac{d}{dy} g^{-1}_{k}(y) \right| \cdot f_X\big(g^{-1}_{k}(y)\big),$$ where $g^{−1}$ is the number of solutions in $x$ for the equation $$g(x) = y$$, and $$g_k^{-1}(y)$$ are these solutions.

Vector to vector
Suppose $n(y)$ is an $n$-dimensional random variable with joint density $x$. If $f$, where $y = G(x)$ is a bijective, differentiable function, then $G$ has density $y$: $$ p_{Y}(\mathbf{y}) = f\Bigl(G^{-1}(\mathbf{y})\Bigr) \left| \det\left[\left.\frac{dG^{-1}(\mathbf{z})}{d\mathbf{z}}\right|_{\mathbf{z}=\mathbf{y}}\right] \right|$$ with the differential regarded as the Jacobian of the inverse of $p_{Y}$, evaluated at $G(⋅)$.

For example, in the 2-dimensional case $y$, suppose the transform $x = (x_{1}, x_{2})$ is given as $G$, $y_{1} = G_{1}(x_{1}, x_{2})$ with inverses $y_{2} = G_{2}(x_{1}, x_{2})$, $x_{1} = G_{1}^{−1}(y_{1}, y_{2})$. The joint distribution for y = (y1, y2) has density $$p_{Y_1, Y_2}(y_1,y_2) = f_{X_1,X_2}\big(G_1^{-1}(y_1,y_2), G_2^{-1}(y_1,y_2)\big) \left\vert \frac{\partial G_1^{-1}}{\partial y_1} \frac{\partial G_2^{-1}}{\partial y_2} - \frac{\partial G_1^{-1}}{\partial y_2} \frac{\partial G_2^{-1}}{\partial y_1} \right\vert.$$

Vector to scalar
Let $$ V: \R^n \to \R $$ be a differentiable function and $$ X $$ be a random vector taking values in $$ \R^n $$, $$ f_X $$ be the probability density function of $$ X $$ and $$ \delta(\cdot) $$ be the Dirac delta function. It is possible to use the formulas above to determine $$ f_Y $$, the probability density function of $$ Y = V(X) $$, which will be given by $$f_Y(y) = \int_{\R^n} f_{X}(\mathbf{x}) \delta\big(y - V(\mathbf{x})\big) \,d \mathbf{x}.$$

This result leads to the law of the unconscious statistician: $$\operatorname{E}_Y[Y] =\int_{\R} y f_Y(y) \, dy = \int_{\R} y \int_{\R^n} f_X(\mathbf{x}) \delta\big(y - V(\mathbf{x})\big) \,d \mathbf{x} \,dy = \int_{{\mathbb R}^n} \int_{\mathbb R} y f_{X}(\mathbf{x}) \delta\big(y - V(\mathbf{x})\big) \, dy \, d \mathbf{x}= \int_{\mathbb R^n} V(\mathbf{x}) f_X(\mathbf{x}) \, d \mathbf{x}=\operatorname{E}_X[V(X)].$$

Proof:

Let $$Z$$ be a collapsed random variable with probability density function $$p_Z(z) = \delta(z)$$ (i.e., a constant equal to zero). Let the random vector $$\tilde{X}$$ and the transform $$H$$ be defined as $$H(Z,X)=\begin{bmatrix} Z+V(X)\\ X\end{bmatrix}=\begin{bmatrix} Y\\ \tilde{X}\end{bmatrix}.$$

It is clear that $$H$$ is a bijective mapping, and the Jacobian of $$H^{-1}$$ is given by: $$\frac{dH^{-1}(y,\tilde{\mathbf{x}})}{dy\,d\tilde{\mathbf{x}}}=\begin{bmatrix} 1 & -\frac{dV(\tilde{\mathbf{x}})}{d\tilde{\mathbf{x}}}\\ \mathbf{0}_{n\times1} & \mathbf{I}_{n\times n} \end{bmatrix},$$ which is an upper triangular matrix with ones on the main diagonal, therefore its determinant is 1. Applying the change of variable theorem from the previous section we obtain that $$f_{Y,X}(y,x) = f_X(\mathbf{x}) \delta\big(y - V(\mathbf{x})\big),$$ which if marginalized over $$x$$ leads to the desired probability density function.

Sums of independent random variables
The probability density function of the sum of two independent random variables $x_{2} = G_{2}^{−1}(y_{1}, y_{2})$ and $U$, each of which has a probability density function, is the convolution of their separate density functions: $$ f_{U+V}(x) = \int_{-\infty}^x f_U(y) f_V(x - y)\,dy = \left( f_{U} * f_{V} \right) (x) $$

It is possible to generalize the previous relation to a sum of N independent random variables, with densities $V$: $$f_{U_1 + \cdots + U}(x) = \left( f_{U_1} * \cdots * f_{U_N} \right) (x)$$

This can be derived from a two-way change of variables involving $U_{1}, ..., U_{N}$ and $Y = U + V$, similarly to the example below for the quotient of independent random variables.

Products and quotients of independent random variables
Given two independent random variables $Z = V$ and $U$, each of which has a probability density function, the density of the product $V$ and quotient $Y = UV$ can be computed by a change of variables.

Example: Quotient distribution
To compute the quotient $Y = U/V$ of two independent random variables $Y = U/V$ and $U$, define the following transformation: $$\begin{align} Y &= U/V \\[1ex] Z &= V \end{align}$$

Then, the joint density $V$ can be computed by a change of variables from U,V to Y,Z, and $p(y,z)$ can be derived by marginalizing out $Y$ from the joint density.

The inverse transformation is $$\begin{align} U &= YZ \\ V &= Z \end{align}$$

The absolute value of the Jacobian matrix determinant $$J(U,V\mid Y,Z)$$ of this transformation is: $$ \left| \det\begin{bmatrix} \frac{\partial u}{\partial y} & \frac{\partial u}{\partial z} \\ \frac{\partial v}{\partial y} & \frac{\partial v}{\partial z} \end{bmatrix} \right| = \left| \det\begin{bmatrix} z & y \\ 0 & 1 \end{bmatrix} \right| = |z|. $$

Thus: $$p(y,z) = p(u,v)\,J(u,v\mid y,z) = p(u)\,p(v)\,J(u,v\mid y,z) = p_U(yz)\,p_V(z)\, |z| .$$

And the distribution of $Z$ can be computed by marginalizing out $Y$: $$p(y) = \int_{-\infty}^\infty p_U(yz)\,p_V(z)\, |z| \, dz$$

This method crucially requires that the transformation from U,V to Y,Z be bijective. The above transformation meets this because $Z$ can be mapped directly back to $Z$, and for a given $V$ the quotient $V$ is monotonic. This is similarly the case for the sum $U/V$, difference $U + V$ and product $U − V$.

Exactly the same method can be used to compute the distribution of other functions of multiple independent random variables.

Example: Quotient of two standard normals
Given two standard normal variables $UV$ and $U$, the quotient can be computed as follows. First, the variables have the following density functions: $$\begin{align} p(u) &= \frac{1}{\sqrt{2\pi}} e^{-{u^2}/{2}} \\[1ex] p(v) &= \frac{1}{\sqrt{2\pi}} e^{-{v^2}/{2}} \end{align}$$

We transform as described above: $$\begin{align} Y &= U/V \\[1ex] Z &= V \end{align}$$

This leads to: $$\begin{align} p(y) &= \int_{-\infty}^\infty p_U(yz)\,p_V(z)\, |z| \, dz \\[5pt] &= \int_{-\infty}^\infty \frac{1}{\sqrt{2\pi}} e^{-\frac{1}{2} y^2 z^2} \frac{1}{\sqrt{2\pi}} e^{-\frac{1}{2} z^2} |z| \, dz \\[5pt] &= \int_{-\infty}^\infty \frac{1}{2\pi} e^{-\frac{1}{2}\left(y^2+1\right)z^2} |z| \, dz \\[5pt] &= 2\int_0^\infty \frac{1}{2\pi} e^{-\frac{1}{2}\left(y^2+1\right)z^2} z \, dz \\[5pt] &= \int_0^\infty \frac{1}{\pi} e^{-\left(y^2+1\right)u} \, du && u=\tfrac{1}{2}z^2\\[5pt] &= \left. -\frac{1}{\pi \left(y^2+1\right)} e^{-\left(y^2+1\right)u}\right|_{u=0}^\infty \\[5pt] &= \frac{1}{\pi \left(y^2+1\right)} \end{align}$$

This is the density of a standard Cauchy distribution.

title: Probability density function