Originally Posted by

**sirellwood** Hi all, having real problems doing this question. Can anyone explain the steps of how its done (leaving the process of actually carrying out the steps to me! :-))

If X1,X2, . . . ,Xn are independent random variables from the Binomial distribution

Bin(k, $\displaystyle \theta$), show that S = $\displaystyle \displaystyle\sum\limits_{i=0}^n i^3$ Xi is sufficient for $\displaystyle \theta$

(i) by using the Factorization Theorem;

(ii) by finding the distribution of X1,X2, . . . ,Xn conditional on S = s.