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

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

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.

2. 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).

3. ## Thanks!

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

Originally Posted by 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).

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