Question: 1) Let X1, X2, ...Xn are i.i.d random sample from N(u, ?) with / unknown but o is known. We know that Xn, the sample

1) Let X1, X2, ...Xn are i.i.d random sample from N(u,

1) Let X1, X2, ...Xn are i.i.d random sample from N(u, ?) with / unknown but o is known. We know that Xn, the sample mean is sufficient for u. (20 points) a) Find the MVUE of u b) Find the MVUE of (Calculate E[X,] and try to find the UE of u+) (Hint: We can write E[X ] = EXn - / + ]4. Explore binomial expansion of (a + b)+. Also note that for any X ~ N(u, 0?), E(X - ()4 = 302 and E(X - ()3 = 0)

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