A distribution describes how values of a variable are spread out. In statistics, it lists each possible value and how often it occurs, or gives the probability of each value. Distributions can be discrete, like the number of heads in ten coin flips, or continuous, like heights in a population.

The normal distribution is the most famous, a bell-shaped curve that appears in many natural phenomena. The binomial distribution counts successes in repeated trials. The Poisson distribution models rare events. Each has its own formula and properties.

Distributions are summarized by their mean, variance, and shape. They are used to test hypotheses, estimate probabilities, and model uncertainty. In machine learning, distributions describe data and model outputs. Understanding distributions is fundamental to statistics and to any field that deals with data.

• Shows possible values and their frequencies
• Can be discrete or continuous
• Normal, binomial, and Poisson are common
• Central to statistics and data analysis