Wikipedia 10K Redux by Reagle from Starling archive. Bugs abound!!!

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RandomVariable

back to ProbabilityDistributions

:DiscreteRandomVariable -- ContinuousRandomVariable

We can think of a random variable as a numeric result of operating a non-deterministic mechanism. The mechanism can be as simple as a coin or die to be tossed or a rapid counter which cycles many times in the interval of a typical human physical reaction time. Mathematically, we can describe it as a function whose domain is a SampleSpace and whose range is some SeT of numbers.

We can specify a random variable by specifying its CumulativeDistributionFunction because two random variables with identical cdf's are isomorphic. From the cdf, we can calculate probabilities for any events which can be described as countable intersections and unions of intervals.
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DickBeldin