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.
Read more about Probability Mass Function: Formal Definition, Examples
Famous quotes containing the words probability, mass and/or function:
“Crushed to earth and rising again is an author’s gymnastic. Once he fails to struggle to his feet and grab his pen, he will contemplate a fact he should never permit himself to face: that in all probability books have been written, are being written, will be written, better than anything he has done, is doing, or will do.”
—Fannie Hurst (1889–1968)
“All great art, and today all great artlessness, must appear extreme to the mass of men, as we know them today. It springs from the anguish of great souls. From the souls of men not formed, but deformed in factories whose inspiration is pelf.”
—Alexander Trocchi (1925–1983)
“The fact remains that the human being in early childhood learns to consider one or the other aspect of bodily function as evil, shameful, or unsafe. There is not a culture which does not use a combination of these devils to develop, by way of counterpoint, its own style of faith, pride, certainty, and initiative.”
—Erik H. Erikson (1904–1994)