Solve the problem.A particle moves every second on the x-axis in one-unit jumps such that its coordinate at any time is 0, 1, 2, or 3. If the particle is at 0 or 3, it does not move. On the other hand, if it is at 1 or 2, it will move to the right with probability
and to the left with probability
.(a) Give the stochastic matrix of transitions for this process in standard form.(b) Determine the stable matrix.(c) What is the probability that the particle will end up at 0 if it starts at 2?(d) What is the probability that the particle will end up at 0 if it starts at 1?
What will be an ideal response?
(a) | ![]() | (b) |
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(c) | ![]() |

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