Ex. I: Suppose that the sample mean of 100 iid Poisson variables is 3.2. Find an approximate 95%-confidence interval for the unknown parameter theta of the Poisson distribution.

Ex. II: Suppose that X_1,...,X_n are iid normal with known (!) mean and unknown variance v. Find an MVUE for v.

Ex. III: Suppose that X_1,...,X_n are iid with density f(x; theta)=(2theta^3)^(-1)*x^2*exp(-x/theta) for x>0. Find an MVUE for theta. You may use without proof that X_1 has mean 3theta and second moment 12theta^2.

Ex. IV: Suppose that X_1,...,X_n are iid normal with known mean 0 and unknown variance v. Use the delta method to determine the asymptotic distribution of the MLE of log(v). Work out the details.