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CO4 Home Assignment-2.pdf

CO4 Home Assignment-2.pdf - Probability and Stochastic...

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Probability and Stochastic Models CO4 Home Assignment-2 1. There are three categories of income tax filers in the United states: those who never evaded taxes, those who sometimes do it, and those who always do it. An examination of audited tax returns from one year to the next shows that of those who did not evaded taxes last year, 95% continue in the same category this year, 4% move to the “sometimes” category, and the remainder move to the ”always” category. For those who sometimes evade taxes, 6% move to “never”, 90% stay the same, and 4% move to “always”. As for the “always” evaders, the respective percentages are 0%, 10% and 9 0%. a) Express the problems as a Markov chain. b) Determine the long run percentages of “never”, “sometimes” and “always” tax categories? 2. A small grocery store has only one checkout counter. Customers arrive at this counter at random that are 1 to 4 minutes apart. Each possible value of inter arrival time has the same probability of occurrence. The service times vary from 1 to 4 minutes, with the probabilities shown in the following table Service time(minutes 1 2 3 4 Probability 0.15 0.45 0.25 0.15 Simulate for 10 arrivals to determine i) average waiting time of customer.
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