Imperfections in an optical fiber are distributed according to a Poisson process such that the distance between imperfections in meters has an exponential distribution with parameter 2m 1 (a) What is the expected distance between imperfections ' (b) What is the probability that the distance between...

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Imperfections in an optical fiber are distributed according to a Poisson process such that the distance between

Question:

Imperfections in an optical fiber are distributed according to a Poisson process such that the distance between imperfections in meters has an exponential with parameter λ. = 2m-1.
(a) What is the expected distance between imperfections.'
(b) What is the probability that the distance between two imperfections is longer than I meter?
(c) What is the of the number of imperfections in a 3-meter stretch of fiber?
(d) What is the probability that a 3-meter stretch of fiber has no more than four imperfections?
(This problem is continued in Problem 4.3.5.)
Distribution
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