2. A Poisson random variable takes non-negative integer values. If the parameter is A, then E(X ) = A and Var(X) = A. Given a sample X1, ..., Xn, the maximum likelihood of A is the sample mean AMLE = 1 ELI Xi = Xn. (a) Mathematically, what are the bias and variance of the MLE of 1. (b) Using the CLT, find a 90% CI for A as a function only of n and the MLE AMLE