Independence of random variables

Two or more random variables may be defined as independent in much the same way as events. Some random variables for are independent iff prob

for all , i.e. the joint CDF is the product of individual CDFs

Discrete random variables

In the case of discrete random variables the above is equivalent to

for all .

A common phrase is independent and identically distributed, often abbreviated as i.i.d..

Conditional independence

Random variables are conditionally independent given a random variable iff

for all and .