4 Sum of independent random variables (5p) Let X be a normal random variable with expected value 0 and standard deviation 1. Let Y be a discrete random variable with the following distribution: | P(Y=-1) | P(Y=1) Assume that X and Y are independent. 1. Compute the density function of variable Z = X Y (2p) 2. Compute the correlation between X and Z (1p) 3. Is X+Z normally distributed? (1p) 4. Are X and Z independent? (1p)