Random Variables

A random variable—unlike a normal variable—does not have a specific value, but rather a range of values and a density that gives different probabilities of obtaining values for each subset. This can be used to model uncertainty, whether from incomplete or simplified models. Random variables are used extensively in areas such as social science, science, engineering, and finance. The Wolfram Language uses symbolic distributions to represent a random variable. In the Wolfram Language, you can directly compute several dozen properties from symbolic distributions, including finding the probability of an arbitrary event or simulating it to generate data. The Wolfram Language has the largest collection of parametric distributions ever assembled, and parametric distributions can be automatically estimated from data. The Wolfram Language provides nonparametric distributions directly computed from data, automating and generalizing the many nonparametric methods in use for specific properties. Distributions can be derived from other distributions or given by formulas for distribution functions, giving infinite extensibility to the whole framework.

Probability — compute probabilities of predicates given distributions

Expectation — compute expectations of expressions given distributions

NProbability ▪ NExpectation ▪ Distributed () ▪ Conditioned ()