The diagrams below show three Markov chains, where arrows indicate a non-zero transition probability.

A bus containing 100 gamblers arrives in Las Vegas on a Monday morning. The gamblers play only poker or blackjack, and never change games during the day. The gamblers' daily choice of game can be modeled by a Markov chain: 95% of the gamblers playing poker today will play poker tomorrow, and 80% of the gamblers playing blackjack today will play blackjack tomorrow. (a) Write down the stochastic (Markov) matrix corresponding to this Markov chain. (b) If 60 gamblers play poker on Monday, how many gamblers play blackjack on Tuesday? (c) Find the unique steady-state vector for the Markov matrix in part (a).

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Shakira's concerts behave like a Markov chain. If the current concert gets cancelled, then there is an 90% chance that the next concert will be cancelled also. However, if the current concert does not get cancelled, then there is only a 50% chance that the next concert will be cancelled. What is the long-run probability that a concert will  not be cancelled? a. 1/4 b. 1/10 c. 1/6 d. 1/2 e. 5/6 f. None of the others are correct

Answer the following questions.

Alan and Betty play a series of games with Alan winning each game independently with probability p = 0.6. The overall winner is the first player to win two games in a row.  Define a Markov chain to model the above problem.

Suppose a Markov Chain has transition matrix % 0 % % If the system starts in state 3, what is the probability that it goes to state 2 on the next observation, and then goes to state 4 on the following observation? (A) 24 (B) 1 (C) 4 (D) ½24 (E) % (F) %32 (G) 0 (H) %

In a hotel, each employee is in one of three possible job classifications, and changes that classifications (independently) according to a Markov chain with transition probabilities. What percentage of employees are in each classification?