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A team of researchers published an article on the study of how vehicles are dispatched based...

A team of researchers published an article on the study of how vehicles are dispatched based on an airport-based taxi service. The researchers modeled this system with an underlying assumption that travel times of successive trips to and from the terminal are independent exponentially distributed random variables with ? = 15 ???????.

  1. (a) Find the mean and standard deviation of trip time distribution

  2. (b) How likely is it for a particular trip to take more than 25 minutes?

  3. (c) If two taxis are dispatched together, what is the probability that both of them will be

    gone for more than 25 minutes?

  4. (d) what is the likelihood of at least of one of the taxis returning within 25?

Math   Statistics-And-Probability   
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Answer #1

It is given that travel times of successive trips to and from the terminal are independent exponentially distributed random variables with ? = 15 ???????. .

The CDF is .

a) The mean of the distribution is .

The standard deviation of the distribution is .

b) The required probability is

c) The required probability is

.

d) The likelihood (probability)of at least of one of the taxis returning within 25 is the complement of the probability calculated in part (c).

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