Question

Thousands of runners participate in the Peachtree Road Race every year in Atlanta. To ensure that the race is fair, runners usually start based on their expected race times, with the fastest group of runners starting first and the slowest group of runners starting last. Suppose that you are watching the fastest group of runners, which is comprised of 50 runners. Further, suppose that the time it takes each of the runners in this group to finish is an independent exponential random variable with mean 45 minutes. You are a spectator who will leave after the first 3 runners from this group cross the finish line. If T is the amount of time you are watching the race, find E[T] and Var(T).

          Thousands of runners participate in the Peachtree Road Race every year in Atlanta. To ensure that the race is fair, runners usually start based on their expected race times, with the fastest group of runners starting first and the slowest group of runners starting last. Suppose that you are watching the fastest group of runners, which is comprised of 50 runners. Further, suppose that the time it takes each of the runners in this group to finish is an independent exponential random variable with mean 45 minutes. You are a spectator who will leave after the first 3 runners from this group cross the finish line. If T is the amount of time you are watching the race, find E[T] and Var(T).

Added by Roberto M.

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