If $X_1,X_2$ constitute a random sample of size n=2 from a Poisson Population show that the mean of the sample is a sufficient estimator of the parameter $\lambda$ .
Since the sum of Poissons is also Poisson with parameter $\lambda+\lambda=2\lambda$
Then $E[Y]=2\lambda$. where Y constitute of two Poisson distributions each with parameter $\lambda$.
Do I have to show that $2\lambda$ is sufficient for $\lambda$.
I don't understand what the estimator is here?