Problem 1* (a) Let X1, ... , Xn be a random sample from a Poisson(a) distribution. Decide whether the following estimato

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Problem 1 A Let X1 Xn Be A Random Sample From A Poisson A Distribution Decide Whether The Following Estimato 1 (41.69 KiB) Viewed 27 times

Problem 1* (a) Let X1, ... , Xn be a random sample from a Poisson(a) distribution. Decide whether the following estimators are unbiased for the parameter 1 for some value of the constant c: (i) Un(X) = cX.. (ii) Vn(X) = c(X1 + Xn). (b) Compute Var(Un) and Var(Vn) (with c's found in Part (a)) and then argue that Un is a consistent sequence of estimators for p but Vn is not. (c) Let X1,..., X, be a random sample from some distribution with mean y = 0 and variance o2 (unknown). Find the value of the constant c so that In T(Ă) = . x is an unbiased estimator for o?. a 72 с n i=1