Recall Problem 4.2.6 concerning imperfections in an optical fiber. Suppose that five adjacent imperfections are located on

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Recall Problem 4.2.6 concerning imperfections in an optical fiber. Suppose that five adjacent imperfections are located on a fiber.
(a) What is the distribution of the distance between the first imperfection and the fifth imperfection?
(b) What is the expectation of the distance between the first imperfection and the fifth imperfection'.'
(c) What is the standard deviation of the distance between the first imperfection and the fifth imperfection'.'
(d) Consider the probability that the distance between the first imperfection and the fifth imperfection is longer than three meters. Show how this probability can be obtained using the gamma distribution and also by using the Poisson distribution.
Distribution
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