Math Help - Continuous random variables question.

1. Continuous random variables question.

I know that c =1. Easy enough to do. I don't know how to do the rest though.

2. 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)

3. OK, if you insist. Here it comes, ready or not...

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

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

Tired now, need sleep... $f(zzzzzzzzzzzzzzzzzzzzzzzzzzzzz$

4. Thank you! I thought that might be it, but it seemed too easy!