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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
 

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=1 X2
i ), T2(X1, . . . , Xn) = n
i=1 Xi,
T3(X1, . . . , Xn) = n
i=1 X2
i ? Why?
2. Let X1, . . . , Xn be a random sample from a beta distribution with parameters and
: (+)
()()
f(x|, ) =
(+)
()()
x-1

  

Source: Arcones, Miguel A. - Department of Mathematical Sciences, State University of New York at Binghamton

 

Collections: Mathematics