I ran into some problems with this:

Suppose that two electronic components in the guidance system for a missile operate independently and that each has a length of life governed by the exponential distribution with mean 1 (measured in hundreds of hours). Find the pdf for the average length of life of the two components.

I've tried to create a function of these two variables => U = Y1+Y2

which gives E(Y1+Y2) = 2

and then tried to use that f(y) for an exponential distribution is 1/beta *e^-y/beta. I then try to put in beta = 2 and put up an integral:

but it doesn't seem like I'm heading in the right direction. Cam someone please help me out? Thanks a lot!