Question: Let X1, . . . , Xn be a random sample from the following distribution P (X = 1) = P (X = 1) =

Let X1, . . . , Xn be a random sample from the following distribution P (X = 1) = P (X = 1) = , P (X = 0) = 1 2, where is unknown. (a) Show that Tn = n i=1 |Xi| is suicient statistic for (b) Find the MLE of . (c) Calculate the Cramer Rao lower bound for . (d) Does the variance of the MLE achieve the Cramer Rao lower bound

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