The major question in this chapter is: What is the probability of exactly X successes in N trials??

The outcome of the experiment is X successes.

When each number of successes X is paired with its probability of occurrence Af, the set of pairs Af, is a probability function called a binomial distribution.

The several trials of a binomial experiment produce a new random variable X, the total number of successes, which is just the sum of the random variables associated with the single trials.

Their sum is X, the total number of successes, which in this experiment has the value Af.

For the case of a purely inertial autonavigator consisting of three restrained gyros, a coordinate system is used where the sensitive axis of the X accelerometer is parallel to the east-west direction at the base point, and the Y accelerometer sensitive axis is parallel to the north-south direction at the base point.

The input axis of the X gyro, when pointing in the east-west direction, is always perpendicular to the spin axis of earth.

* If it is required to use a single number X as an estimate for the value of numbers, then the arithmetic mean does this best, in the sense of minimizing the sum of squares ( x < sub > i </ sub > − X )< sup > 2 </ sup > of the residuals.

A choice function is a function f, defined on a collection X of nonempty sets, such that for every set s in X, f ( s ) is an element of s. With this concept, the axiom can be stated:

Each choice function on a collection X of nonempty sets is an element of the Cartesian product of the sets in X.

If the method is applied to an infinite sequence ( X < sub > i </ sub >: i ∈ ω ) of nonempty sets, a function is obtained at each finite stage, but there is no stage at which a choice function for the entire family is constructed, and no " limiting " choice function can be constructed, in general, in ZF without the axiom of choice.

For example, suppose that each member of the collection X is a nonempty subset of the natural numbers.

For example, suppose that X is the set of all non-empty subsets of the real numbers.

* 1929 – X. J. Kennedy, American poet and author

* 1966 – Derek Sherinian, American keyboard player, composer, and producer ( Planet X, Dream Theater, and Black Country Communion )

* 1960 – Tony MacAlpine, American guitarist, composer, and producer ( Planet X, CAB, Ring of Fire, and Seven the Hardway )

Conversely, British English favours fitted as the past tense of fit generally, whereas the preference of American English is more complex: AmEng prefers fitted for the metaphorical sense of having made an object " fit " ( i. e., suited ) for a purpose ; in spatial transitive contexts, AmEng uses fitted for the sense of having made an object conform to an unchanged object that it surrounds ( e. g., " fitted X around Y ") but fit for the sense of having made an object conform to an unchanged object that surrounds it ( e. g., " fit X into Y "); and for the spatial senses ( both intransitive and transitive ) of having been matching with respect to contour, with no alteration of either object implied, AmEng prefers fit (" The clothes fit.

Coming of age was dealt with in Good Will Hunting ( 1997 ), race relationships were a theme in American History X ( 1998 ), and the AIDs epidemic and discrimination were the focus of Philadelphia ( 1993 ).

* 2011 – Francis " Frank " X. McDermott, American Republican Party politician ( b. 1924 )

* 1957 – Jerry Gaskill, American musician ( King's X )

In American cinema, directors Kevin Smith, Richard Linklater and Todd Solondz have been called Generation X filmmakers.

The earliest association between anime and adult animation occurred prior to the 1972 release of Fritz the Cat when American distributors attempted to cash in on the publicity garnered from the rating by rushing out dubbed versions of two other adult animations from Japan, both of which featured an X rating in their advertising material: Senya ichiya monogatari and Kureopatora, retitled One Thousand and One Arabian Nights and Cleopatra: Queen of Sex, respectively.

* 1883 – Francis X. Bushman, American actor ( d. 1966 )

* 1971 – Russell Allen, American singer-songwriter ( Symphony X, Adrenaline Mob, Allen-Lande, and Star One )

* 1936 – Betty Shabazz, American educator and activist, wife of Malcolm X ( d. 1997 )

* 1968 – Michael Romeo, American musician ( Symphony X )

The American scholar of religious studies Michael F. Strmiska argued that the modern adoption of the term " Pagan " was " a deliberate act of defiance " against traditional, Christian-dominated society, comparing it to the adoption of the surname " X " amongst African-Americans or the term " queer " amongst LGBT people.

Since 2005 Apple Inc .' s Mac OS X operating system has come bundled with a dictionary application and widget which credits as its source " Oxford American Dictionaries ", and contains the full text of NOAD2.

* American progressive metal band Symphony X interprets multiple scenes of the epic in their song, The Odyssey ( 2002 ).

* 1924 – Francis " Frank " X. McDermott, American Republican Party politician ( d. 2011 )

Public Enemy is an American hip hop group consisting of Chuck D, Flavor Flav, Professor Griff and his S1W group, DJ Lord ( DJ who replaced Terminator X in 1999 ), and Music Director Khari Wynn.

She then starred on the short-lived television series, CBS's Live to Dance, which lasted one season in 2011, and was subsequently a judge on the first season of American version of The X Factor with her former American Idol co-judge Simon Cowell which premiered on September 21, 2011.

Later that year, fellow American Idol judge Simon Cowell invited her to be a guest judge at some of the early auditions for the third series of his similar UK talent show The X Factor.

On May 8, 2011, it was announced that Abdul would rejoin Simon Cowell on the first season of the American version of The X Factor.

Corresponds to " Precambrian X " rocks of older North American geology.

* 1950 – Doug Pinnick, American singer-songwriter and bass player ( King's X )

In fact, Idol had been a member of the punk band Generation X from 1976 – 1981, which was named after Deverson and Hamblett's 1965 sociology book Generation X — a copy of which was owned by Idol's mother.

She acquired a love of rock music during the 1970s, having been introduced by a babysitter to the music of the Los Angeles punk rock band X, which proved a life-changing experience.

As hardcore became the dominant punk rock style, many bands of the older California punk rock movement split up, although X went on to mainstream success and The Go-Go's, part of the Hollywood punk scene when they formed in 1978, adopted a pop sound and became major stars.

X achieved limited mainstream success but influenced various genres of music, including punk rock and folk rock.

Such themes bear similarities to those addressed by punk rock musicians and the perceptions of Generation X.

By 1979, Black Flag were joined by other Los Angeles-area bands playing hardcore punk, including X, Fear, The Germs and the Circle Jerks ( featuring Black Flag's original singer, Keith Morris ).

These include " America's Waltz King " Wayne King, professional wrestler Tommy Treichel, Billy Zoom ( Tyson Kindell ) founding member and original guitarist of the punk band X, MLB player Pete Lister, and former NASA astronaut Dale Gardner.

Many of the Bromley Contingent went on to form bands themselves including The Banshees and Generation X. Arguably they had greater influence than Malcolm McLaren's shops and Vivienne Westwood's designs in shaping the development and look of the early UK punk movement.

Recent Chicano punk bands include Rayos X, Tuberculosis, Mata Mata, Mugre, Venganza and Asko from southern California, La Grita and La plebe from Northern California, as well as Los Crudos from Chicago.

Writing all his own songs, and continuing to perform mostly outside traditional country music channels, Yoakam did many shows in rock and punk rock clubs around Los Angeles, playing with roots rock or punk rock acts like The Blasters ( Yoakam scored a small video hit with his version of their song " Long White Cadillac "), Los Lobos, and X.

The band played support to rising punk stars Generation X in Edinburgh two weeks later.

They were formed as a punk band and had roots in the L. A. punk community ; they shared a rehearsal space with X, and Carlisle ( under the name " Dottie Danger ") had briefly been a member of punk-rock band The Germs.

* X ( 1980s Los Angeles punk, with country and rockabilly influences )

Los Angeles ' original late 1970s punk scene received less press attention than their counterparts in New York or London, but it included cult bands The Screamers, The Germs, The Weirdos, The Dils, The Bags, 45 Grave ( founded by Paul B. Cutler ) and X.

The band ( already fixtures on the West Coast punk scene ) formed alliances with mostly-male punk bands such as Blondie, The Ramones and The Dead Boys ( via New York City's CBGB ) as well as the British punk scene by hanging out with the likes of The Damned, Generation X and The Sex Pistols.

By 1992 the band's success in Japan made an international breakthrough appear likely, leading to an American record contract with Atlantic Records and the renaming of the band from X to X Japan, in order to distinguish from the American punk group X.