Stochastic Models in Operations Research Middle East Technical University, Fall 2016 Study Set 1 1) A naturalist is observing the behavior of a frog in a small lily pond. There are four lily pads in the pond, and the frog jumps from one to another. The probability of jumping from any pad to another pad is inversely proportional to the relative distance. The matrix shows the distances: a) Model the frog’s location as a Markov Chain. Provide the state definition and the state space clearly. Provide the transition probability matrix. b) If the frog starts on pad 2, what is the probability that it is on pad 3 after two jumps? c) In the long run, in what fraction of the time the frog is on pad 1? d) Find and interpret all mean first passage times. 2) Rent-a-Car Company has hired a young IE to describe the way its

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