# finding a distribution

• Oct 25th 2013, 01:43 PM
Keroro
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)
• Oct 25th 2013, 02:10 PM
HallsofIvy
Re: finding a distribution
So $\displaystyle \phi$ is a constant determining the distribution and x is the random variable?
• Oct 25th 2013, 02:19 PM
Keroro
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.
• Oct 27th 2013, 10:27 AM
Shakarri
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
• Nov 10th 2013, 12:07 AM
matheagle
Re: finding a distribution
Just compare this to the chi-square density in your book.