# limiting distribution

• March 1st 2010, 11:50 AM
ankuoli
limiting distribution
Let X1,....,Xn be a random sample from a Poisson( $\lambda$) distribution.

Find the limiting distribution of $\overline{X^2}$.

I found the mean to be E( $\overline{X^2}$) = $(1/n)*E(X_i)^2$

but then i don't know which method to use.

Thank you
• March 1st 2010, 04:26 PM
matheagle
The square is a continuous function.

Since $\bar X\to \lambda$

we have $\left(\bar X\right)^2\to \lambda^2$

and I don't understand what this.... $(1/n)*E(X_i)^2$ means
I guess zero as n goes to infinity