Refer to Example 1 in Section 9.1, where we found the following transition matrix for an insurance company:

If these probabilities remain valid over a long period of time, what percentage of drivers are expected to have an accident during any given year?

Data from Example 1 Section 9.1

An insurance company found that on average, over a period of 10 years, 23% of the drivers in a particular community who were involved in an accident one year were also involved in an accident the following year. They also found that only 11% of the drivers who were not involved in an accident one year were involved in an accident the following year. Use these percentages as approximate empirical probabilities for the following:

Draw a transition diagram.

Find the transition matrix P.

If 5% of the drivers in the community are involved in an accident this year, what is the probability that a driver chosen at random from the community will be involved in an accident next year? Year after next?

Transcribed Image Text:

P = A A' A 23 23 .11 A' 77 .89_ A = accident. A' = no accident