Question

3. A spider hunts a fly moving between the positions 1 and 2 according to a Markov Chain P= 0.3 0.7 The fly, independently of the spider, moves between 1 and 2 according to a second Markov with transition matrix 0.0.3 Chain whose transition matrix is 0.4 0.6 0.6 0.4 The hunt finishes the first time both the spider and the fly are on the same position, (a) Describe the hunt with a suitable 3 states Markov Chain; (b) Assuming that at time 0 the fly is in 1 and the spider in 2, what is the probability that the spider catches the fly in one of the first three moves?

Answer 1

Let {0,1,2} be the state space of hunt.

Here 0 represents that hunt is finished

1 represents that spider is in position 1 and fly is in position 2

2 represents that spider is in position 2 and fly is in position 1

Let Yn and Zn represent the markov chains of spider and fly.

Let Xn represent the markov chain of hunt.

PGw-@iy na@) p(Zn1,-OR.-0)

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