Summary: Math 502. 5th Homework. Due Friday, April 4, 2008.
Show all your work. If a question says find a complete sufficient statistic, you need to
prove that the statistic is complete and sufficient.
1. Let X1, . . . , Xn be a random sample from a Poisson distribution with parameter,
> 0. Find a minimal sufficient statistic for . Which one of the next statistics are
sufficient for : T1(X1, . . . , Xn) = ( n
i=1 Xi, n
i ), T2(X1, . . . , Xn) = n
T3(X1, . . . , Xn) = n
i ? Why?
2. Let X1, . . . , Xn be a random sample from a beta distribution with parameters and
f(x|, ) =