Distribution function

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distribution function

(Also called probability distribution function.) A function F(x) yielding the probability that a stated random variable will assume some value less than or equal to any arbitrary number x.

By definition, the distribution function is identically zero for all values of x below the least admissible value of the random variable, and identically unity for all values of x equal to or greater than the greatest admissible value of the random variable. Moreover, F(x2) ≥ F(x1) whenever x2 > x1. Sometimes, for the sake of clarity, the distribution function is called the cumulative distribution function.
Compare probability density function.

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