Please help with this distribution problem

[mathmajor13]

Say we have X and Y, both of which are independent normal variables of mean zero and variance one. They have joint density

What is the distribution of (X,Y)|Z when

So my idea is that the answer is e^-1/2 chi(0, 2*Z) since f from above =e^-z*e^-1/2
Is this right? If not, how do you do this?
Thanks!

 

[mmm4444bot]

You've posted this exercise three times.

I deleted the two duplicate threads.

Are you having difficulties understanding the web site?