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I'm just brushing up my math skills and I came across the following problem.

A lifetime X of a certain device is exponential with parameter $\mu$ years. What is the expected value of $\max\{\mu/2 , X\}$?

I have no clue on how to start solving this. Any ideas?

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    Your edit is truly mystifying. The new version does not make sense and also makes the answer appear disjointed.2011-10-16
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    I have rolled back your last edit and cleaned it up a bit. I hope you don't mind. Please check that it reads as intended.2011-10-16

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