As you see from the title, I'm having trouble understanding a problem from the 142 SOA Exam 1/P question bank:
A machine consists of two components, whose lifetimes have the joint density function
f(x,y) = 1/50 x>0, y>0, x+y<10)
The machine operates until both components fail. Calculate the expected operational time of the machine....
I solved for E[x+y] over 0<x<10 and 0<y<10-x and got 6.7. This is one of the possible answers but not the correct one, which is 5.0. They offer an explanation but I don't really understand it.... could anyone offer me a clear explanation of how to solve this?
Thanks and good lookin' out people.