Question

Probability problems..

Answer 1

Let X ∈ exponential (1) and Y ∈ exponential (1/2) be independent random variables. We are introducing
S = X + Y

How do I find frequency function g (s) for S?

Answer 2

I know the answer is \[1/2\int\limits_{0}^{s}e^{-s+t}e^{-t/2}dt\] because it is at multiple choice task, but why?