Let X and Y be two N0-valued random variables such that X = Y + Z , where Z is a Bernoulli random variable with parameter p (0 , 1), independent of Y...

Let X and Y be two N0-valued random variables such that X = Y + Z, where Z is a Bernoulli random variable with parameter p ∈ (0,1), independent of Y . Only one of the following statements is true. Which one?

X + Z and Y + Z are independent

X has to be 2N0 = {0,2,4,6,...}-valued (c) The support of Y is a subset of the support of X

E[(X + Y )Z] = E[(X + Y )]E[Z].

none of the above