Let X₁,..., Xn Exp(A) and let AMLE be the MLE estimator. We know that (you can find these facts on Wikipedia) •X := ΣX ~Γ(η, λ) if Y~ Exp(A) then aY~ Exp(x/a) .. aX~I(n,x/a) (a) Check that Q = XX meets the criteria of a pivotal statistic (and say what the distribution of is while you do so). (b) Let qo be the associated quantile for Q such that P(Q≤ a) = (1) (c) Rearrange equation (1) into P(A ≤)=a. Since the parameter space is A > 0, this gives a confidence interval X € [0,...]. = α (d) What is a 95% confidence interval for the data in problem 3? Note: we can compute 90.95 in R. with qgamma (0.95, shape=4, rate=1) = 7.753657 (shape = n, rate = X).