Probability Distribution

A probability distribution describes how the total probability of 1 is spread across all the possible values of a random variable. For a die it is flat (each face gets 1/6); for human heights it is a bell-shaped curve clustered around the average.

Distributions are the vocabulary of statistics: naming the right one lets you compute probabilities, expected values, and the chance of extreme outcomes. For discrete variables we list a probability per value (a probability mass function); for continuous variables we use a density curve where area, not height, gives probability.