Let Y₁, Y2,... be independent random variables with E (Y₂) = a, Var(Y;) = 6² for j≥ 1, and M≥ 0 an integer-valued random variable with E (M)=c, Var(M)= d², independent of the sequence {Y}. Let ZM = Y₁++ YM with Zo = 0. (d) Consider the case where the Yis are equal to -1 with probability 1/2 and 1 with probability 1/2 and where M has a Poisson distribution with parameter A. What is Cov(ZM, M)? (e) Giving your reasons, state whether Z and M in part (d) are independent.