Show that the mean of a random sample of size n is a minimum variance unbiased estimator of "lambda", of a Poisson distribution.

Can anybody provide some help for me?

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- Feb 17th 2010, 07:32 AMkesk717variance unbiased estimator
Show that the mean of a random sample of size n is a minimum variance unbiased estimator of "lambda", of a Poisson distribution.

Can anybody provide some help for me? - Feb 17th 2010, 11:56 AMstatmajor
You'll need to use the Lehmann–Scheffé theorem which states that if Y is a complete sufficient statistic for lambda, and there exists a function of Y such that this function is an unbiased estimator of lambda, then this function is an MVUE of lambda.

1. Find a complete sufficient statistic (Y) for lambda

2. Find a function of Y such that this function is an unbiased estimator of lambda. - Feb 19th 2010, 01:52 PMkesk717
Can somebody give me some more detailed advice? I am still having trouble with this

- Feb 19th 2010, 02:09 PMstatmajor
Fine. Here's a hint: The complete sufficient statistic for a poisson distribution is $\displaystyle \Sigma^n_1 X_i = n \overline{X}$. What's the expecation of $\displaystyle \Sigma^n_1 X_i$?