Cumulative distribution function

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The Cumulative Distribution Function (abbreviated cdf) describes the probability distribution of a quantitative Random Variable, X, completely. For every possible value, x, in the range, the cdf is given by

F(x) = Pr[X<=x],

that is the probability that X is no greater than x.

If X is a Discrete Random Variable, then the probability is concentrated on discrete points and F(x) can be described as a sequence of pairs <x,p(x)> where p(x) = Pr[X=x].

If X is a Continuous Random Variable, the the Probability Density, f(x), is distributed over an interval (or collection of intervals) and can be described as the derivative of F(x) with respect to x.