please answer question three and bonus with specific steps.

3. Suppose that X1, X2, .. .An are independent normal variates with the same variance o', but with different means, X; ~ N(ubi, 02), for i = 1,2, .. .n where bi, b2, ...bn are known constants. (a) Find expressions for the MLE of / and o. You need not show the second derivative conditions. (b) Suppose that bi = b2 =... = bn. Find a simplified expression for the MLE of /. (c) Suppose that bi = b2 =. .. = bn = 1, and / is known. Find the MLE of o. Bonus Question: Suppose X ~ Xia), Y - X ~ X(5) ; Cov(X, Y) = 7. What is E(Y ) and Var(Y)? Does Y follow a Chi-squared distribution? Justify your answer. Hint: Cov(X, Y = W) = Cov(X, Y) = Cov(X, W), Cov(X, X) = Var(X)