Question

The productivity of the gardening season depends on the soil condition. The soil condition falls in one of the three states: (1) good, (2) fair, and (3) poor. Over the years, a gardener has observed that, without using fertilizer, the soil condition can either deteriorate or stay the same but never improve. If this year's soil is good, there is a 30% chance it will stay good next year, a 40% chance it will become fair, and a 30% chance it will deteriorate to a poor condition. If this year's soil condition is fair, next year's condition may remain fair with probability 40% or become poor with probability 60%. Finally, a poor condition this year can only lead to a poor condition next year (with probability 1).

1. Form a Markov chain with states 1-good, 2-fair, and 3-poor to represent the situation. Write the transition matrix.
2. Is this Markov chain an absorbing Markov chain? If yes, identify the absorbing state(s) and the transient state(s).
3. Given that the current soil condition is good, what are the probabilities that the soil condition will be good, fair and poor, respectively, in 2 years from now?
4. In the long run, what is the probability that the soil will end up in the a poor condition (Probability of Absorption)? On the average, how long will it take for the soil condition to become poor? (Time to absorption)
5. On the average, how many years will the soil condition be good and be fair, before becoming poor?

PLEASE HELP SHOW WORK PLEASE

Answer 1

3- 5D2 3-p o.3 o on 0 Ansnwe

clearty e cev to We Crn move to 13-/bro γ 1.2 to

Defin, tyan sien Sta가- Ya en Le

T or

2 2 04 о.С 02 04 0.05 0.28. о.С3 0.1 08 60 2. Avy