The concept of a random walk can be applied to a wide variety of fields such as statistical physics, finance, biology, and psychology. The following problem is a simplified version of a random walk: A particle moves on a line and at any time is located at one of the integers 0, 1, 2, 3, 4, 5. If the particle arrives at 0 or 5, it stays there. Otherwise, after each second, it moves to the right with probability 12 or to the left with the same probability.
(a) Set up the absorbing stochastic matrix, with columns and rows labeled 0, 5, 1, 2, 3, and 4, that describes the transitions.
(b) Find the stable matrix.
(c) What is the probability that a particle beginning at location 3 will eventually be absorbed at location 0?
(d) For a particle beginning at location 4, determine the expected number of times that it will be at location 4 before it is absorbed.

Transcribed Image Text:

Note: -1 .4" .8 1.6 1.2 1.2 2.4 1.6 .8 1 2.4 1.2 1.6 .8 1.2 1.6 4 ||