In this problem we consider a shared-ride van service which provides rides from

Question

In this problem we consider a shared-ride van service which provides rides from an airport into a city. Suppose that the service takes passengers to N dierent 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 variable with mean 5, what is the expected number of stops?

Explanation / Answer

a)

Expected number of stops is = 10 * 0.75 = 7.5

Expected number of stops is = 6 *0.85 = 5.1

b)

expected number of stops for a poisson variable is mean = 5

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