In probability theory and statistics, a probability mass function (pmf) is a function that gives the probability that a discrete random variable is exactly equal to some value. The probability mass function is often the primary means of defining a discrete probability distribution, and such functions exist for either scalar or multivariate random variables, given that the distribution is discrete.
A probability mass function differs from a probability density function (p.d.f.) in that the latter is associated with continuous rather than discrete random variables; the values of the latter are not probabilities as such: a p.d.f. must be integrated over an interval to yield a probability.
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Famous quotes containing the words probability, mass and/or function:
“Only in Britain could it be thought a defect to be “too clever by half.” The probability is that too many people are too stupid by three-quarters.”
—John Major (b. 1943)
“The hard truth is that what may be acceptable in elite culture may not be acceptable in mass culture, that tastes which pose only innocent ethical issues as the property of a minority become corrupting when they become more established. Taste is context, and the context has changed.”
—Susan Sontag (b. 1933)
“As a medium of exchange,... worrying regulates intimacy, and it is often an appropriate response to ordinary demands that begin to feel excessive. But from a modernized Freudian view, worrying—as a reflex response to demand—never puts the self or the objects of its interest into question, and that is precisely its function in psychic life. It domesticates self-doubt.”
—Adam Phillips, British child psychoanalyst. “Worrying and Its Discontents,” in On Kissing, Tickling, and Being Bored, p. 58, Harvard University Press (1993)