Problem 3. A discrete-time Markov chain is known to be a birth-death process with three states- the probabilities P01 =

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Problem 3 A Discrete Time Markov Chain Is Known To Be A Birth Death Process With Three States The Probabilities P01 1 (45.31 KiB) Viewed 33 times

Problem 3. A discrete-time Markov chain is known to be a birth-death process with three states- the probabilities P01 = P12 P10 = 0.2 but P21 is unspecified. Let X, denote the state at time k = 0, 1, 2,..... For each of the following statements, either determine the possible value(s) of probability P21 or explain why no such value exists: (a) Upon entering state 2, the expected time it takes to first exit state 2 is equal to 100. (b) The probability P(X₂ = 2|Xo = 2) is equal to 0.28. (c) Given no self-transitions ever occur, the probability P(X4 = 0|Xo = 0) is equal to 0.5. (d) The steady-state probability associated with state 1 is equal to 0.25. (e) The long-term expected frequency of deaths is equal to 0.3. (f) State 2 is an absorbing state. (g) The mean recurrence time of state 2 is equal to 6.