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Unformatted text preview: rts with two working light bulbs.
Suppose that when both are working, one of the two will go out with probability
.02 (each has probability .01 and we ignore the possibility of losing two on the
same day). However, when only one is there, it will burn out with probability
.05. (i) What is the long-run fraction of time that there is exactly one bulb
working? (ii) What is the expected time between light bulb replacements?
1.37. An individual has three umbrellas, some at her o ce, and some at home.
If she is leaving home in the morning (or leaving work at night) and it is raining,
she will take an umbrella, if one is there. Otherwise, she gets wet. Assume that
independent of the past, it rains on each trip with probability 0.2. To formulate
a Markov chain, let Xn be the number of umbrellas at her current location. (a)
Find the transition probability for this Markov chain. (b) Calculate the limiting
fraction of time she gets wet.
1.38. Let Xn be the number of days since David last shaved, calculated at
7:30AM when he i...
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