the probability distribution is a function that gives the probabilities of different outcomes for an experiment.
if is a discrete random variable then the list of values that it could receive and their corresponding probabilities are called the distribution law, probability law, or the distribution of said variable
let be a random variable.
- the probability measure is called the distribution of .
- for a real random variable , the map is called the distribution function of (or, more accurately, of ). we write if and say that has distribution .
- a family of random variables is called identically distributed if for all . we write if ( for distribution).