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Unformatted text preview: Assignment 12 1. Let M n denote the sequence of sample means form an iid random process X n : M n = X 1 + X 2 + ··· + X n n (a) Is M n a Markov process? (b) If the answer to part a is yes, find the following state transition pdf: f M n ( X  M n 1 = y ). 2. (a) Show that the following autoregressive process is a Markov process: Y n = rY n 1 + X n Y = 0 where X n is an iid process. (b) Find the transition pdf if X n is an iid Gaussian sequence. 3. Let X n be an iid random process. Show that X n is a Markov process and give its onestep transition probability matrix. 4. A very popular barbershop is always full. The shop has two barbers and three chairs for waiting, and as soon as a customer completes his service and leaves the shop, another enters the shop. Assume the mean service time is m . (a) Use Little’s formula to relate the arrival rate and the mean time spent in the shop. (b) Use Little’s formula to relate the arrival rate and the mean time spent in service....
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 Winter '10
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 Probability theory, $1, Markov chain, $5

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