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In this problem we consider a shared-ride van service (e.g., SuperShuttle, though the problem descrip- tion...

  1. In this problem we consider a shared-ride van service (e.g., SuperShuttle, though the problem descrip- tion here doesn’t quite describe what SuperShuttle does) which provides rides from an airport into a city. Suppose that the service takes passengers to N different hotels or other possible destinations in the city.(a) If the number of passengers showing up for a given van is P ∼ Binomial(12, p), and each passenger independently selects one of the N destinations, what is the expected number of stops that the van will make? Find numerical values for N = 10 and p = 0.75, and N = 6 and p = 0.85. (b) Supposing, slightly irrationally, that the number of passengers is instead a Poisson random vari- able with mean 5, what is the expected number of stops?

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