Let X1 and X2 be iid Poisson(X) random variables. Show that TX+2X2 is not a sufficient...

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Let X1 and X2 be iid Poisson(X) random variables. Show that TX+2X2 is not a sufficient statistic for >. (Hint: the Factorization Theorem uses the word if and only if. Alternatively, find a minimal sufficient statistic S and show that S is not a function of T.) Let X1 and X2 be iid Poisson(X) random variables. Show that TX+2X2 is not a sufficient statistic for >. (Hint: the Factorization Theorem uses the word if and only if. Alternatively, find a minimal sufficient statistic S and show that S is not a function of T.)