2.2 Examples Certain types of discrete random variables occur frequently, and we list some of these.

Throughout this section, n is a positive integer, p is a number in [0, 1], and q = 1 − p.

We never describe the underlying probability space.

Bernoulli distribution. This is the simplest non-trivial distribution. We say that the discrete random variable X has the Bernoulli distribution with parameter p if the image of X is {0, 1}, so that X takes the values 0 and 1 only.

Such a random variable X is often called simply a coin toss. There exists p ∈ [0, 1] such that P(X = 0) = q, P(X = 1) = p, (2.13)

and the mass function of X is given by