160a_machine_ex - Questions 1) Set-up this problem as a...

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Winter 2010 Pstat160A Hand-out MC #7 Vending machines problem There are 2 soda vending machines in the entrance hall of a dormitory. Suppose that these vending machines are filled regularly so they never run out of soda. However, they sometimes stop functioning. More precisely, on any given day, a machine breaks independently of the other with probability .1. If one machine is down, it takes an average of 5 days to be fixed, and assume that the time for repair follows a Geometric distribution. However, when both machines are broken, an emergency repair person comes on the same day and fixes one of the machines (so the machine is down for only 1 day), and the other machine is repaired as normally scheduled. When both machines are working, the total sale is $150/day, but when only one is up, the sales are only $100/day (think for instance that they sell different drinks and not every one is willing to switch).
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Unformatted text preview: Questions 1) Set-up this problem as a Markov Chain. Argue why all underlined assumptions are valid. 2) What is the proportion of time during which both machines are down? both up? 3) What are the average sales per month. 4) Suppose, at a given time both machines are working. What is the expected time before both are broken? 5) Suppose that both machine are down. What is the probability that both are up before one gets broken again? 6) Suppose now that one machine has probability .1 of failing, the other .2. Answer questions 1) to 3) as above. 7) Going back to the original assumptions, assume now that the emergency repair person doesnt come on the same day, but the next day (so that the machine is down for 2 days). Answer questions 1)-3)....
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This note was uploaded on 01/10/2011 for the course STAT 160A taught by Professor Bonnet during the Winter '10 term at UCSB.

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