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April 24th, 2016, 11:38 PM   #1
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Exponential Distribution

I am having trouble setting up the solution to the following problem.

In a mile race between $\displaystyle A$ and $\displaystyle B$, the time it takes $\displaystyle A $ to complete the mile is an exponential random variable with rate $\displaystyle λ_a$ and is independent of the time it takes
$\displaystyle B$ to complete the mile, which is an exponential random variable with rate $\displaystyle λ_b$. The one who finishes earliest is declared the winner and receives $\displaystyle Re^{−αt}$ if the
winning time is $\displaystyle t$, where $\displaystyle R$ and $\displaystyle \alpha$ are constants. If the loser receives $\displaystyle 0$, find the expected amount that runner $\displaystyle A$ wins.

Thank you for any help
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April 26th, 2016, 06:44 PM   #2
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when it says receives $\displaystyle 0$, what is the the $\displaystyle 0$ referring to?
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