Random Variate

A random variate is a particular outcome of a random variable: the random variates which are other outcomes of the same random variable would have different values. Random variates are used when simulating processes driven by random influences (stochastic processes). In modern applications, such simulations would derive random variates corresponding to any given probability distribution from computer procedures designed to create random variates corresponding to a uniform distribution, where these procedures would actually provide values chosen from a uniform distribution of pseudorandom numbers.

Procedures to generate random variates corresponding to a given distribution are known as procedures for random variate generation or pseudo-random number sampling.

In probability theory, a random variable is a measurable function from a probability space to a measurable space of values that the variable can take on. In that context, and in statistics, those values are known as a random variates, or occasionally random deviates, and this represents a wider meaning than just that associated with pseudorandom numbers.