Consider the gamma distribution f(x)=(B^a)/gamma(a) *x^(-a-1)*e^(-B/x) show that this is exponential family with both a and B are unknown parameters. B.for the iid sample x1...Xn from this distribution propose a complete sufficient statistic T from the distribution family.

C. Show that this is an exponential family distribution when B is unknown parameter and a is fixed and unknown. D. For an iid sample x1...Xn from this distribution propose a complete sufficient statistic T for the distribution family.

E. Using a gamma distribution properties find a sampling distribution of T.

F. Propose a UMVUE for B and justify how you know it is