# Continuous random variables question.

• Aug 26th 2009, 06:16 AM
DCU
Continuous random variables question.
http://img412.imageshack.us/img412/5656/maths.jpg

I know that c =1. Easy enough to do. I don't know how to do the rest though.
• Aug 26th 2009, 01:26 PM
DCU
I really need help with this urgently. I've an exam in the morning and it could come up. Any help would be greatly appreciated.

Ignore part(a)
• Aug 26th 2009, 03:42 PM
halbard
OK, if you insist. Here it comes, ready or not...

You could try $\displaystyle f_{X+Y}(z)=\frac{\mathrm d}{\mathrm dz}\mathrm P(X+Y\leq z)$, where perhaps $\displaystyle \mathrm P(X+Y\leq z)=\int_{X+Y\leq z}f_{X,Y}\mathrm dA=\int_{-\infty}^\infty\int_{-\infty}^{z-y}f_{X,Y}(x,y)\mathrm dx\mathrm dy$.

So maybe $\displaystyle f_{X+Y}(z)=\int_{-\infty}^\infty f_{X,Y}(z-y,y)\mathrm dy$.

Tired now, need sleep... $\displaystyle f(zzzzzzzzzzzzzzzzzzzzzzzzzzzzz$
• Aug 26th 2009, 11:32 PM
DCU
Thank you! I thought that might be it, but it seemed too easy!(Rofl)