In statistics, an exchangeable sequence of random variables (also sometimes interchangeable) is a sequence X1, X2, X3, ... (which may be finitely or infinitely long) whose joint probability distribution does not change when the positions in the sequence in which finitely many of them appear are altered.

In probability theory, calculation of the sum of normally distributed random variables is an instance of the arithmetic of random variables.

In probability theory and statistics, a collection of random variables is independent and identically distributed (i.i.d., iid, or IID) if each random variable has the same probability distribution as the others and all are mutually independent.

In probability theory, there exist several different notions of convergence of sequences of random variables, including convergence in probability, convergence in distribution, and almost sure convergence.