We have seen a number of theorems concerning sufficiency and related concepts for exponential families. Let X1,..., Xn(n > 2) be a random sample for each of the following distribution families, and...

Extracted text: We have seen a number of theorems concerning sufficiency and related concepts for exponential families. Let X1,..., Xn(n > 2) be a random sample for each of the following distribution families, and establish the following results. (b) The statistic T(X) = E, X? is minimal sufficient in the N(14, 14) family. (d) The statistic T(X) = (E, X,, E, x?) is minimal sufficient for 0 = (14, o) in the N(u,0) family. 1 3