I am trying to find the pdf of the ratio of two RV's . is chi-square distributed with two degrees of freedom and is non-central chi-sqaure distributed with 2 degrees of freedom and non centrality parameter . How to find the pdf of ? Any thoughts?

Another dumb question:

Also, If , and if and are normal distributions with different mean and variances, can I write W as and solve by finding the pdf of first and then finding the pdf for ?

Any suggestion will be really appreciated.

Thanks

Arvind