# How to find point estimator for $\lambda$ in Poisson distribution?

Suppose we have a random sample $$(X_1,X_2,...,X_n)$$ from a Poisson distribution $$Poi(\lambda)$$.

How to find a point estimator of $$\lambda$$, and compute the mean and variance of the estimator.

Actually, I am confused that how to find $$\lambda$$. It is because I think that the mean and variance is the $$\lambda$$. Is it correct?

So, can anyone tell me how to find $$\lambda$$? Thank you.

"A" point estimator doesn't have to be the "best" point estimator that takes into account all the information. So you can just take the mean of the sample, this is a point estimator of $$\lambda$$.
• Is that the mean and variance of Poisson distribution is the point estimator now? I am not sure that I am correct or not. I just know that the mean and variance of Poisson distribution is $\lambda$. Apr 2 '20 at 8:34
• An "estimator" is a rule for estimating a parameter ($\lambda$) from a given sample, see en.wikipedia.org/wiki/Estimator.
• I calculate that the value of mean and variance of the estimator are $\lambda$, is it correct? Apr 2 '20 at 9:43