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Unformatted text preview: tion? (c) They are amorous now.
What is the expected amount of time until depression sets in?
4.29. A small company maintains a ﬂeet of four cars to be driven by its workers
on business trips. Requests to use cars are a Poisson process with rate 1.5 per
day. A car is used for an exponentially distributed time with mean 2 days.
Forgetting about weekends, we arrive at the following Markov chain for the
number of cars in service.
2 (a) Find the stationary distribution. (b) At what rate do unfulﬁlled requests
come in? How would this change if there were only three cars? (c) Let
g (i) = Ei T4 . Write and solve equations to ﬁnd the g (i). (d) Use the stationary
distribution to compute E3 T4 .
4.30. A submarine has three navigational devices but can remain at sea if at
least two are working. Suppose that the failure times are exponential with
means 1 year, 1.5 years, and 3 years. Formulate a Markov chain with states 0
= all parts working, 1,2,3 = one part failed, and 4 = two failures. Compute...
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).
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