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2.14. 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. What is the average length of time the
boat can remain at sea.
2.15. Excited by the recent warm weather Jill and Kelly are doing spring
cleaning at their apartment. Jill takes an exponentially distributed amount of
time with mean 30 minutes to clean the kitchen. Kelly takes an exponentially
distributed amount of time with mean 40 minutes to clean the bath room. The
ﬁrst one to complete their task will go outside and start raking leaves, a task
that takes an exponentially distributed amount of time with a mean of one hour. 94 CHAPTER 2. POISSON PROCESSES When the second person is done inside, they will help the other and raking will
be done at rate 2. (Of course the other person may already be done raking in
which case the chores are done.) What is the expected time until the chores
are all done?
2.16. Ron, Sue, and Ted arrive at the beginning of a professor’s o ce hours.
The amount of t...
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 Spring '10
 DURRETT
 The Land

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