4. A machine works for an exponentially distributed time with rate u and then fails. A repair crew checks the machine at times distributed according to a Poisson process with rate A; if the machine is found to have failed then it is immediately replaced. Find the expected time between replacements of machines.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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4. A machine works for an exponentially distributed time with rate u and then fails. A repair
crew checks the machine at times distributed according to a Poisson process with rate A; if the
machine is found to have failed then it is immediately replaced. Find the expected time between
replacements of machines.
Transcribed Image Text:4. A machine works for an exponentially distributed time with rate u and then fails. A repair crew checks the machine at times distributed according to a Poisson process with rate A; if the machine is found to have failed then it is immediately replaced. Find the expected time between replacements of machines.
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