# Ratio Distribution

#### arvind

I am trying to find the pdf of the ratio of two RV's $$\displaystyle Z = X/Y$$. $$\displaystyle X$$ is chi-square distributed with two degrees of freedom and $$\displaystyle Y$$ is non-central chi-sqaure distributed with 2 degrees of freedom and non centrality parameter $$\displaystyle \lambda$$. How to find the pdf of $$\displaystyle Z$$? Any thoughts?
Another dumb question:
Also, If $$\displaystyle W= X^2/Y^2$$, and if $$\displaystyle X$$ and $$\displaystyle Y$$ are normal distributions with different mean and variances, can I write W as $$\displaystyle (X/Y)^2$$ and solve by finding the pdf of $$\displaystyle G = X/Y$$ first and then finding the pdf for $$\displaystyle W = G^2$$?

Any suggestion will be really appreciated.

Thanks
Arvind

#### mr fantastic

MHF Hall of Fame
I am trying to find the pdf of the ratio of two RV's $$\displaystyle Z = X/Y$$. $$\displaystyle X$$ is chi-square distributed with two degrees of freedom and $$\displaystyle Y$$ is non-central chi-sqaure distributed with 2 degrees of freedom and non centrality parameter $$\displaystyle \lambda$$. How to find the pdf of $$\displaystyle Z$$? Any thoughts?
Another dumb question:
Also, If $$\displaystyle W= X^2/Y^2$$, and if $$\displaystyle X$$ and $$\displaystyle Y$$ are normal distributions with different mean and variances, can I write W as $$\displaystyle (X/Y)^2$$ and solve by finding the pdf of $$\displaystyle G = X/Y$$ first and then finding the pdf for $$\displaystyle W = G^2$$?

Any suggestion will be really appreciated.

Thanks
Arvind
In each case, are X and Y independent?

By the way, I suggest you borrow the classic book by M. D. Springer called The Algebra of Random Variables.

#### matheagle

MHF Hall of Honor
Divide each by 2 and you have an F, BUT there is this noncentrality problem.
So it must be a noncentral F with (2,2) df.