Pdf of sum of two random variables problem

[fourieranalys]

Hi, everybody.

My problem is about Probability and Random Process.

i can't understand the probability density function of sum of two random variables and function of product of two random variables.

Here is my question with a part of a solution:

how can i find these problems solutions and where can i study on the internet ?

 

[╔(σ_σ)╝]

What exactly don't you understand? This is a theorem that is been applied along with a simple integration..

 

[fourieranalys]

why integral goes to 0 and w, how can i determine the bounds of that integral ? how can i determine the shaded area for computing the PDF of W=X+Y ?

 

[╔(σ_σ)╝]

The integration bounds was supposed to be from -infinity to infinity; bascially the minimum x and maximum x. X is at least 0. X= W-y. So x is at most W; corresponding to y=0.