limiting distribution

**ankuoli** · March 1st 2010, 10:50 AM

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

**matheagle** · March 1st 2010, 03:26 PM

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

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