1. Suppose that the length of a phone call in minutes is an exponential random v

Question

1. Suppose that the length of a phone call in minutes is an exponential random variable with parameter = 1/10. If someone arrives immediately ahead of you at a public telephone booth, find the probability that you will have to wait

(a) more than 10 minutes;

(b) between 10 and 20 minutes.

2 .Suppose that the number of miles that a car can run before its battery wears out is exponentially distributed with an average value of 10,000 miles. If a person desires to takea 5000 mile trip, what is the probability that he or she will be able to complete the trip without having to replace the car battery? What can be said when the distribution is not exponential?

Explanation / Answer

1.

a)

As

P(x>c) = 1 - exp(-lambda*c)

Then as lambda = 1/10,

P(x>10) = 1 - exp(-(1/10)*10) = 0.632120559 [ANSWER]

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b)

As

P(a<x<b) = exp(-lambda*a) - exp(-lambda*b)

Hence,

P(10<x<20) = exp(-(1/10)*10) - exp(-(1/10)*20) = 0.232544158 [ANSWER]

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