# Let a 2 s and set a c for b 6 a in s let x0 a x1

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Unformatted text preview: to repair. Formulate a Markov chain model with state space {0, 1, 2, 3} and ﬁnd its stationary distribution. 4.11. Solve the previous problem in the concrete case 3 = 1/84, µ1 = 1/3, µ2 = 1/5, and µ3 = 1/7. 1 = 1/24, 2 = 1/30, 152 CHAPTER 4. CONTINUOUS TIME MARKOV CHAINS 4.12. Three frogs are playing near a pond. When they are in the sun they get too hot and jump in the lake at rate 1. When they are in the lake they get too cold and jump onto the land at rate 2. Let Xt be the number of frogs in the sun at time t. (a) Find the stationary distribution for Xt . (b) Check the answer to (a) by noting that the three frogs are independent two-state Markov chains. 4.13. There are 15 lily pads and 6 frogs. Each frog at rate 1 gets the urge to jump and when it does, it moves to one of the 9 vacant pads chosen at random. Find the stationary distribution for the set of occupied lily pads. 4.14. A computer lab has three laser printers, two that are hooked to the network and one that is used as a spare. A working printer will function for an exponential amount of time with mean 20 days...
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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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