iid Let Y1, Y2, Y3, ..., Y, N(µ, 0²), where o? = 25 is known. 1. Find the asymptotic distribution of Z := where u is the MLE. Hint: what is the asymptotic distribution of i? 2. Suppose now we do not...

Solve parts 1 and 2 of the question below. Show all work.

Extracted text: iid Let Y1, Y2, Y3, ..., Y, N(µ, 0²), where o? = 25 is known. 1. Find the asymptotic distribution of Z := where u is the MLE. Hint: what is the asymptotic distribution of i? 2. Suppose now we do not know o? and instead plug in the MLE estimator ô? :E(Yi – î)² to obtain Z := Is the asymptotic distribution still N(0, 1)? If yes, why? (hint: what do we know about consistency of MLES? Slutsky's theorem?).