Let X and Ybe Bernoulli random variables. Let Z = XY.
a. Show that Z is a Bernoulli random variable.
b. Show that if X and Y are independent, then 
.
(a) Since the possible values of X and Y are 0 and 1, the possible values of the product Z = XY are also 0 and 1.
Therefore Z is a Bernoulli random variable.
(b) 
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