An airport shuttle moves passengers between the airportterminal and the rental c

Question

An airport shuttle moves passengers between the airportterminal and the rental car agency bus stop. The shuttlepicks up all passengers waiting at the bus stop and drops them offat the airport terminal; it then picks up passengers at theterminal and returns to the rental agency bus stop and repeats theprocess.   If there are no customers at the bus stop, theshuttle moves on to the terminal empty. The times betweenreturns to the stop are indpendent random variables withdistribution F, mean , and variance 2. Passengers arrive at the bus stop in accordnace with a Poissonprocess with rate . Suppose the bus has left the stop, andlet X denote the number of passengers it picks up when itreturns. a. Determine E[X] and Var[X] b. At what rate does the shuttle bus arrive at the terminalwithout any passengers? An airport shuttle moves passengers between the airportterminal and the rental car agency bus stop. The shuttlepicks up all passengers waiting at the bus stop and drops them offat the airport terminal; it then picks up passengers at theterminal and returns to the rental agency bus stop and repeats theprocess.   If there are no customers at the bus stop, theshuttle moves on to the terminal empty. The times betweenreturns to the stop are indpendent random variables withdistribution F, mean , and variance 2. Passengers arrive at the bus stop in accordnace with a Poissonprocess with rate . Suppose the bus has left the stop, andlet X denote the number of passengers it picks up when itreturns. a. Determine E[X] and Var[X] b. At what rate does the shuttle bus arrive at the terminalwithout any passengers?

Explanation / Answer

Hello - can you please give me a hint for parts c - e? (c) At what rate does the shuttle bus arrive at the terminalwithout any passengers? Suppose that each passenger that has to wait at the bus stop morethan c time units writes and angry letter to the shuttle busmanager. (d) What proportion of passengers write angry letters? (e) How does your answer to part (d) relate to Fe(x)?

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