Trouble understanding Exam 1/P question from SOA 142... help?

[Robert Jordan]

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)
0 otherwise

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.

[Stodd]

did you try using order statistics? If I'm reading your problem correctly, and you haven't left anything out, I would be looking for E(Z) where z=Max(x,y).

[Robert Jordan]

No I didn't and thank you for your explanation Stodd, I understand it now.

did you try using order statistics? If I'm reading your problem correctly, and you haven't left anything out, I would be looking for E(Z) where z=Max(x,y).