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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.

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"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 $\lambda$.

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  • $\begingroup$ ok, thank you so much $\endgroup$
    – rayray218
    Apr 2, 2020 at 8:27
  • $\begingroup$ 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 $\lambda$. $\endgroup$
    – rayray218
    Apr 2, 2020 at 8:34
  • $\begingroup$ An "estimator" is a rule for estimating a parameter ($\lambda$) from a given sample, see en.wikipedia.org/wiki/Estimator. $\endgroup$
    – Gijs
    Apr 2, 2020 at 8:46
  • $\begingroup$ I calculate that the value of mean and variance of the estimator are $\lambda$, is it correct? $\endgroup$
    – rayray218
    Apr 2, 2020 at 9:43
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    $\begingroup$ You could make this into a separate question, where you show your calculation. $\endgroup$
    – Gijs
    Apr 2, 2020 at 10:57

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