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April 24th, 2016, 11:38 PM  #1 
Senior Member Joined: Jan 2014 Posts: 196 Thanks: 3  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 
April 26th, 2016, 06:44 PM  #2 
Senior Member Joined: Jan 2014 Posts: 196 Thanks: 3 
when it says receives $\displaystyle 0$, what is the the $\displaystyle 0$ referring to?


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