5. Suppose that X1, X,. ... "IP Exp()) for > > 0.3 In this case, it can be shown that, if Yn = min {X1, X2, ..., Xn}, then Yn ~ Exp(nd). Let n = 1/x . Is Zn = nYn an unbiased estimator for n? bill 6. We have three boxes. One box contains two silver coins, one box contains one silver and one gold, and one box contains two gold coins. We randomly sample a box, and then randomly take a coin out of the box. If we've removed a gold coin, what's the chance that the remaining coin is silver? (a) Give an answer to this, assuming that the boxes are equally likely. What is your sample space S In this case (b) Give an answer to this, assuming that the boxes are not equally likely, but your outcomes are. What is your sample space S In this case? 3 Recall that, whenever X ~ Exp(A), E(X) = 1-1 and Var(X) = 1-2