please help

Let Xi, .... Xn be a random sample from the Normal(/, ') distribution, where ur and o' are unknown, and suppose we are interested in testing Ho: / = po versus Hj: p * po. (a) Give the likelihood function L(A, of; X1, ..., X,). (b) Give the log-likelihood function ((A, o'; X1; .... X,). (c) Find the maximum likelihood estimators & and a' of p and o'. (d) Find an expression for of, where on = argmax, L(, o'; X1, ..., Xn). (e) Give the likelihood ratio. (f) Show that the likelihood ratio simplifies to LR(XI, .. ., XA) = (g) Show that for any c c [0, 1] the rejection criterion of the likelihood ratio test, LR(X], . .., X,) c for some c". (h) Use the fact that X1. . ..,X, " Normal(A, o') = V(X, -#)/S, t-1 to find a value of such that the likelihood ratio test has size equal to a for any a c (0, 1)