1. 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 aBernoulli 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 aBernoulli random variable.