Problem 7 (Sufficiency, factorization, and the MLE). Prove the converse of the factorization theorem in the...

Transcribed Image Text:

Problem 7 (Sufficiency, factorization, and the MLE). Prove the converse of the factorization theorem in the discrete case. Namely prove that if X, are i.i.d discrete random variables with probability mass function p(x) and if T is a sufficient statistic for 8, then the joint density can be factored as p(x1,,xn|0) = g(T,0)h(x1,...,xn) Problem 7 (Sufficiency, factorization, and the MLE). Prove the converse of the factorization theorem in the discrete case. Namely prove that if X, are i.i.d discrete random variables with probability mass function p(x) and if T is a sufficient statistic for 8, then the joint density can be factored as p(x1,,xn|0) = g(T,0)h(x1,...,xn)