Question: Consider k = 2 and m = 1. Let X1,..., XnMulti3(1,0), where 0 03. For simplicity, denote X = (X1,..., Xik) and Xio =

Consider k = 2 and m= 1. LetX1, ..., XnMultis(1,6),where?3.For simplicity, denote Xi = (Xi1, ..., Xik) and X 10 =1- (Xi 2. Prove that T(X1:n) = (S1(X1:n), S2(X1:n)) is a sufficient statistic (SS) for 6 by using(a) (15%) the definition of suffi

Consider k = 2 and m = 1. Let X1,..., XnMulti3(1,0), where 0 03. For simplicity, denote X = (X1,..., Xik) and Xio = 1 - (Xi1 + + Xik) for each i. Define the statistics 12 S; (X1:n) = Xij, i=1 j= 0, 1, 2,..., k. 2. Prove that T(X1:n) = (S1(X1:n), S2(X1:n)) is a sufficient statistic (SS) for by using (a) (15%) the definition of sufficiency; (b) (10%) Neyman-Fisher factorization theorem; and (c) (15%) the properties of exponential family.

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