Question: 2. Let Y = 2X +6 where e ~ N(0, 1) and X ~ Unif(-1, 1). Assume that X and e are independent. a. Find

2. Let Y = 2X +6 where e ~ N(0, 1)

2. Let Y = 2X +6 where e ~ N(0, 1) and X ~ Unif(-1, 1). Assume that X and e are independent. a. Find the mean and variance of Y. (4 pts) b. Find E[Y$ ]. Hint: If Z ~ N(0, 1), E(Z*) = 0 for k is odd. (3 pts) c. Find Cou(e, ("). Are e and e independent? (3 pts)

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