To control the traffic during Ramadan month, a Police Sergeant is assigned to control the traffic
at the eight intersections indicated in following figure.

He is instructed to remain at each intersection for an hour and then to either remain at the same
intersection or move to a neighboring intersection. To avoid establishing a pattern, he is told to
choose him new intersection on a random basis, with each possible choice equally likely. For
example, if he is at intersection 3, his next intersection can be 2, 3, 4 or 8, each with probability 1⁄4
[note: he may stay at position 3, or he may go only to neighboring intersections. His neighboring
intersections are 2, 4, and 8 (observe the figure) and he will select one of them. Total probability
is always 1. Total possible choice is 4. So, probability of each intersection is 1⁄4.]. Every day he
starts at the location where he stopped the day before.
Form the transition matrix for this Markov chain.

To complete the table it is necessary to know the possibilities that the sergeant has to change or remain in an intersection. The probabilities (depending on the box) are:

0
0.2
0.25
0.33

How to calculate the probability of intersection change?

To know the probability of intersection change, it is necessary to locate the police officer at one of the intersections. Subsequently, count how many possibilities of change you have, for example: 3 possibilities and finally add the possibility of remaining in the intersection as shown below:

Intersection 3 has 3 possibilities of changing towards intersections 2, 8 and 4. Additionally, it has the possibility of staying at intersection 3, that is, it has 4 possible decisions.

To know the probability we divide the number 1 (because it is only a decision that we have to make) and divide it by the number of possibilities (4).

1 ÷ 4 = 0.25

According to the image we can infer that in some intersections they only have 3, 4 and 5 possibilities, so the probability of change will be different as shown below:

1 ÷ 3 = 0.33
1 ÷ 4 = 0.25
1 ÷ 5 = 0.2

Learn more about probabilities in: https://brainly.com/question/8069952