Consider k = 2 and m = 1. Let X1,..., XnMulti3(1,0), where 0 03. For...

 

 

 

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Consider k = 2 and m = 1. Let X1,..., XnMulti3(1,0), where 0 € 03. For simplicity, denote X₁ = (X₁1,..., 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. Consider k = 2 and m = 1. Let X1,..., XnMulti3(1,0), where 0 € 03. For simplicity, denote X₁ = (X₁1,..., 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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a Let TX1n S1X1n S2X1n be the proposed statistic We want to show that for any the conditi... View the full answer