Question

Let X and Y be Bernoulli random variables. Let Z = XY. Show that Z is a Bernoulli random variable.

Answer 1

Answer:

If X and Y are Bernoulli random variables, the only possible values of Z=XY are 0 and 1 and the probability mass function of the random variable Z takes on the value 0 for any value of Z other than 0 and 1. Therefore, Z is a Bernoulli random variable.