옷 V₁ V₂ V3 Fig. 1. A random walker in a very small town. (2) Suppose that we modify the random walk example in Figure 1 as follows. At each integer time, the random walker tosses two coins. The first coin is to decide whether to stay or go. If it comes up heads, he stays where he is, whereas if it comes up tails, he lets the second coin decide whether he should move one step clockwise, or one step counterclockwise. Write down the transition matrix, and draw the transition graph, for this new Markov chain. Thanks so much in advance.

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M1

V4
V3
Fig. 1. A random walker in a very small town.
(2) Suppose that we modify the random walk example in Figure 1 as follows. At
each integer time, the random walker tosses two coins. The first coin is to decide
whether to stay or go. If it comes up heads, he stays where he is, whereas if it
comes up tails, he lets the second coin decide whether he should move one step
clockwise, or one step counterclockwise. Write down the transition matrix, and
draw the transition graph, for this new Markov chain.
Thanks so much in advance.
of
Transcribed Image Text:V4 V3 Fig. 1. A random walker in a very small town. (2) Suppose that we modify the random walk example in Figure 1 as follows. At each integer time, the random walker tosses two coins. The first coin is to decide whether to stay or go. If it comes up heads, he stays where he is, whereas if it comes up tails, he lets the second coin decide whether he should move one step clockwise, or one step counterclockwise. Write down the transition matrix, and draw the transition graph, for this new Markov chain. Thanks so much in advance. of
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