freedom 2. Markov Chain (see figure above) Consider a rat in a maze with 4 cells
ID: 3053831 • Letter: F
Question
freedom 2. Markov Chain (see figure above) Consider a rat in a maze with 4 cells, indexed as 1,2,3,4, and the outside (freedom), indexed by 0 (that can only be reached via cell 4). The rat starts initially in a given cell and then takes a move to another cell, continuing to do so until finally reaching eom. We assume that at each move (transition) the rat, independent of the past, is equally likely to choose from among the neighboring cells (sharing an edge), eg. if it is in cell 4, then it is equal likely that the rat moves to cell 3, 2, or freedom. Please answer the following quesitons: (a) write out the state space for the rat's move (b) write out the transition matrix for the rat's moves (c) (optional) what's the probability that the rat event ually gets freedom?Explanation / Answer
(a). State space for rat's move is State1, State 2, State 3, State 4 & State 0(Freedom).
(b) Transition matrix:
0 1 2 3 4
0 1 0 0 0 0
1 0 0 1/3 1/3 1/3
2 0 1/3 0 1/3 1/3
3 0 1/3 1/3 0 1/3
4 1/4 1/4 1/4 1/4 0
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