Suppose X1, ..., Xn form a random sample from Poisson()), where > > 0 is unknown. Note that the value o = e-^ corresponds to the probability that an observation from this Poisson distribution has the value 0. For i = 1, ..., n, define Yi = 1, if Xi = 0, 0, otherwise, and consider the estimator 6 = _ _"_, Yi of 0. (a) Show that T = EX; is a sufficient statistic for A. (b) Since 6 is not a function of 7, the Rao-Blackwell theorem implies that E[ | 7'] is an improved estimator of 6. Find E[6 | 7]