# Univariate probability distributions

In probability and statistics, a probability distribution assigns a probability to every possible collection of outcomes of a random experiment. Examples are found in experiments whose sample space is non-numerical, where the distribution would be a categorical distribution; experiments whose sample space is encoded by discrete random variables, where the distribution is a probability mass function; and experiments with sample spaces encoded by continuous random variables, where the distribution is a probability density function.

A probability distribution can be specified in a number of different ways, each of which are equivalent, often chosen for mathematical convenience:

1. by supplying a valid probability mass function or probability density function
2. by supplying a valid cumulative distribution function or survival function
3. by supplying a valid hazard function
4. by supplying a valid characteristic function
5. by supplying a rule for constructing a new random variable from other random variables whose joint probability distribution is known.

Important and commonly encountered probability distributions include the binomial distribution, the hypergeometric distribution, and the normal distribution.