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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