# Math Help - finding a distribution

1. ## finding a distribution

Given a random sample from population with density function f(x; ø) = √(ø) exp[-øπx²]

Prove that 2πøx² is distributed as X²(1) ( chi square with 1 degree of freedom).

How would I approach this using moments generating function?
[Originally ø is meant to be a symbol for lamda)

2. ## Re: finding a distribution

So $\phi$ is a constant determining the distribution and x is the random variable?

3. ## Re: finding a distribution

Ø is the parameter . Like how lamda is the parameter for the poisson or how mu and sigma are parameters of the normal distribution.

4. ## Re: finding a distribution

I am pretty sure that a Chi squared random variable is equal to a normally distributed random variable squared.
Show that x is normally distributed then show that 2πøx² has one degree of freedom

5. ## Re: finding a distribution

Just compare this to the chi-square density in your book.