# Thread: Finding joint density function

1. ## Finding joint density function

I have some questions on finding joint pdf. For example, I am to find the pdf of H = |X| + |Y| where X and Y are 2 standard normal pdf. I first found the pdf of |X| and |Y| which I get as just 2 times the standard normal pdf. And then I do a convolution integrating from 0 to infinity to try to get H. But I cant seem to integrate the function. Is this the right way to approach problems like this? And is H a guassian? Thanks for any help

2. Hello,

H is not gaussian : it's never negative !

Have you tried with cdfs ?

3. Thanks for the reply. I have another question regarding functions of random variable. If X is a random variable where the pdf of X, f(x)=xexp(-0.5x^2) x>0 and f(x)=0 x<0. If Y= -X, am I right to say that the pdf of y, g(y)= -yexp(-0.5y^2) y<0, g(y)=0, y>0. Thanks for any help, I am not very good at this

4. Yes it's correct ! Use the Jacobian transformation for pdf (I think it's called this way, you may look after it on google).