Question: Let X,,X2, . ,Xn be a random sample from N(u, 1), where u E (-0, c0). For any real number x, let sgn(x) =

Let X,,X2, . ,Xn be a random sample from N(u, 1), where

Let X,,X2, . ,Xn be a random sample from N(u, 1), where u E (-0, c0). For any real number x, let sgn(x) = 1, if x 2 0; sgn(x) = 0, if x < 0. (a) Is T1 (X) = X a sufficient statistic for u? (b) Is T, (X) = X3 + 2X a minimal sufficient statistic for ? .... (c) Is T3 (X) = (IXI, sgn(X)) a sufficient statistic for u? %3D

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