# Square root of Poisson Distribution

• Aug 9th 2010, 03:58 PM
southprkfan1
Square root of Poisson Distribution
Let $\displaystyle Y_n$ be a sequence of Poisson distributed random variables with mean n*u. Let $\displaystyle X_n = {Y_n}^{1/2}$. Find the limiting distribution of $\displaystyle X_n$ after properly standardized.

I'm pretty sure that X should be normally distributed and the answer should use the CLT in some way. All I have so far is that:

$\displaystyle P(X=x) = \frac{e^{-nu}(nu)^{x^2}}{{x^2}!}$

And now i'm pretty much stuck
• Aug 9th 2010, 05:56 PM
mr fantastic
Quote:

Originally Posted by southprkfan1
Let $\displaystyle Y_n$ be a sequence of Poisson distributed random variables with mean n*u. Let $\displaystyle X_n = {Y_n}^{1/2}$. Find the limiting distribution of $\displaystyle X_n$ after properly standardized.

I'm pretty sure that X should be normally distributed and the answer should use the CLT in some way. All I have so far is that:

$\displaystyle P(X=x) = \frac{e^{-nu}(nu)^{x^2}}{{x^2}!}$

And now i'm pretty much stuck

Is this relevant: http://www.tina-vision.net/docs/memos/2001-010.pdf
• Aug 9th 2010, 08:27 PM
southprkfan1
Quote:

Originally Posted by mr fantastic

Thanks for the link, but I didn't really find it helpful (or maybe it's just late and I'm tired). It also appears to take a lot of information for granted.