(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose X has a Poisson distribution with parameter lambda. Given a random sample of n observations,

Find the MLE of lambda, and hat lambda.

Find the expected value and variance of hat lambda.

Show that hat lambda is a consistent estimator of lambda.

2. Relevant equations

PX(x) = e^-lambda.lambda^x/x!

E(X) = lambda ??? or mean

var (X) = lambda ?? or mean

3. The attempt at a solution

I am really struggling with stats, hope someone can help.

I try to find likelihood function

L(x1,x2,...,xn|lambda) = e^-lambda.lambda^x/x!

= capital pi from i=1 to n, e^-lambda.lambda^xi/xi!

then I'm stuck.

Differentiating with respect to lambda,

-e^-lambda.xlambda^(x-1)/x!

is that the answer???

sorry about the notation also, is there somewhere on this site to get the symbols?

Any help greatly appreciated.

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# Homework Help: Maximum likelihood of Poisson distribution

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