Question: Let X and Y be Bernoulli random variables. Let Z = X + Y. a. Show that if X and Y cannot both be equal

Let X and Y be Bernoulli random variables. Let Z = X + Y.

a. Show that if X and Y cannot both be equal to 1, then Z is a Bernoulli random variable.

b. Show that if X and Y cannot both be equal to 1, then pZ = pX + pY.

c. Show that if X and Y can both be equal to 1, then Z is not a Bernoulli random variable.

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