Quiz question In a psychology experiment7 a random number of people. X , volunteer to be studied. Each of them is randomly assigned to either the control group (with probability 0.2) or the treatment group (with probability 0.8), all independently. Let Y be the number of people assigned to the treatment group. The distribution of X is unknown. However, we know that E(X) = 40 and Var(X) = 25. Hint: use Theorem 8.10 on page 163: Cov(X, Y) = C0V(X,IE (Y | X)). (6) Find Var(Y). Hint: use the Variance Partition Formula: Var(Y) = E(Var(Y l X)) + Var(lE(Y l X, see Theorem 8.11 on page 163. What is the conditional variance for the conditional dis tribution you found in part (a)? (f) Find any