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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 until stopped. Mathematically, we can describe it as a function whose ___domain is a [[Probability/Sample space|sample space]] and whose range is some [[set]] of numbers.
We can always specify a random variable by specifying its [[cumulative distribution function]] 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.
:[[discrete random variable]] -- [[continuous random variable]]
back to [[probability distribution]]
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What about random variables whose range is not numerical? These random variables do not have CDF's. Similarly, while the CDF for a random variable whose range is more than one-dimensional can be defined, it is much more difficult to deal with. -- TedDunning
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Someone should probably add something about [[Markov chain]]s here. -- [[Buttonius]]
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