Random variables and probability distributions are two of the most important concepts in statistics. A random variable assigns unique numerical values to the outcomes of a random experiment; this is a process that generates uncertain outcomes. A probability distribution assigns probabilities to each possible value of a random variable.

The two basic types of probability distributions are discrete and continuous. A discrete probability distribution can only assume a finite number of different values.

Examples of discrete distributions include:

  • Binomial

  • Geometric

  • Poisson

A continuous probability distribution can assume an infinite number of different values. Examples of continuous distributions include:

  • Uniform

  • Normal

  • Student's t

  • Chi-square

  • F