Probability distribution function

In probability theory, the cumulative distribution function (CDF), also called probability distribution function or just distribution function, completely describes the probability distribution of a real-valued random variable X. For every real number x, the CDF of X is given by where the right-hand side represents the probability that the random variable X takes on a value less than or equal to x. The probability that X lies in the interval (a, b] is therefore F(b) − F(a) if a < b. It is conventional to use a capital F for a cumulative distribution function, in contrast to the lower-case f used for probability density functions and probability mass functions.
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