Question: Let $X_1, X_2, ... , X_n$ be a random sample from a Poisson distribution with parameter $\theta$. Show that $Y = $$\sum_{i=1}^n X_i$ is a complete and sufficient statistic for $\theta$ .
I used factorization theorem to prove that $Y = $$\sum_{i=1}^n X_i$ is a a sufficient statistic. By definition,$Y = $$\sum_{i=1}^n X_i$ is complete if $E_\theta$$\sum_{i=1}^n X_i=0$ for all $\theta$. However, I just don't know where to start to show that it is complete.
Any suggestion or step-by-step answer is really appreciated. Thanks all!
[self-study]
tag. Also add the source of the exercise. Thank you. – Reviewer $\endgroup$ – Jim May 16 '18 at 10:40