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**chutiya** Let $\displaystyle X_1,\cdots,X_n$ be a random sample from $\displaystyle N(\mu,\mu^2)$. Show that $\displaystyle T=(\sum_{i=1}^n X_i,\sum_{i=1}^n {X_i}^2) \mbox{is minimum sufficient but not complete}$.

so, I did the first part to show that T is a minimum sufficient statistic. But I am confused on how to show that it is not complete. How can I find a non zero function using t that does not depend on mu? I am confused on the expected value part. Could anyone help?

Thanks.