Let X1, X2, ..., Xn be a sample from a population X following a Poisson distribution with parameter / > 0: P(X = k) = e-ulik k! k = 0,1,2, ... Recall that E (X) = Var(X) = / and let X be the sample mean. This question aims at the estimation of the parameter p = P(X = 0) = e . Define two estimators of p as n P1 = I(x; = 0) and P2 = e-* n j=1 (a) Show that p, is a consistent estimator of p. [4] (b) Show that p, is asymptotically normal and give the mean and the variance of this limiting distribution