Probability Mass Function

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:

    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)

    No man’s thoughts are new, but the style of their expression is the never-failing novelty which cheers and refreshes men. If we were to answer the question, whether the mass of men, as we know them, talk as the standard authors and reviewers write, or rather as this man writes, we should say that he alone begins to write their language at all.
    Henry David Thoreau (1817–1862)

    Uses are always much broader than functions, and usually far less contentious. The word function carries overtones of purpose and propriety, of concern with why something was developed rather than with how it has actually been found useful. The function of automobiles is to transport people and objects, but they are used for a variety of other purposes—as homes, offices, bedrooms, henhouses, jetties, breakwaters, even offensive weapons.
    Frank Smith (b. 1928)