Finding Variance of Sample Mean of Poisson Distribution

[EvLer]

How do I approach finding variance of sample mean of Poisson distribution?
thanks.

 

[radou]

How do I approach finding variance of sample mean of Poisson distribution?
thanks.

You can certainly start with looking at the definition of variance.

 

[EvLer]

I did: Var(X) = E(X²) - (E(X))²
the problem is that this is given for rv X, not X' or X-bar, that's where i get lost.
I know that last term is lambda².
Actually what I need to find for this problem is E(X'²), i.e.
E(X'²) = Var(X') + lambda²

 

[EvLer]

ok, last question, pleeeease some one look i can't find much on this anywhere and the book does not say much... i don't have intuition for these things...
can I say that sample variance is sum(lambda)/n?
I found something that said sample variance is Sum(Var[X]) of whatever it is the RV divided by n...

 

[radou]

According to my old lecture notes, the sample variance for (X1, ..., Xn) is defined with $$\frac{1}{n} \sum_{i=1}^n(X_{i}-\overline{X})^2$$, where $$\overline{X} = \frac{1}{n}\sum_{i=1}^n X_{i}$$ , and, in your case X~P(lambda).

 

[HallsofIvy]

Yes, the Poisson distribution depends on a single parameter and has the property that both mean and standard distribution are equal to that parameter.