Referring to the Markovian transition matrix in Table 21.6, what is the probability that a section with a PCR value of 77 in the current year will have a PCR value between 60 and 69 (a) one year later, and (b) two years later.

Question

What will be an ideal response?

Answer 1

(a) According to the transition matrix, the section is currently in state 7. Therefore,
the probability of dropping to state 6 (PCR between 60 and 69) in the next year is
0.30.
(b) To predict the condition two years ahead, one will have to apply the matrix
twice, and consider all possibilities as follows:
A section currently in state 7 can in one year:
? remain in state 7 with a probability of 0.60
? drop to state 6 with the probability of 0.30
? drop to state 5 with a probability of 0.10
For the second year:
? A section in state 7 can drop to state 6 with a probability of 0.30
? A section in state 6 can remain in state 6 with a probability of 0.50
? A section in state 5 can move to state 6 with a probability of 0.00
Therefore, the probability of that section currently in state 7 of being in state 6 two
years later can be calculated as:
Probability = (0.60)(0.30) + (0.30)(0.50)
Probability = 0.33
The probability of the given section being in state 6 in two years is 0.33.