2. Every year, during the March through September growing season, a gardener use

Question

2. Every year, during the March through September growing season, a gardener uses a chemical test to check soil condition. Depending on the outcome of the test, productivity for the new season can be one of three good, fair, and poor Over the years, the gardener has observed that the last year's soil condition impacts current year's productivity and that the situation can be described by the following Markov chain Poor Good 0.3 0.1 Fair 0.6 0.6 0.4 0.1 Good Fair Poor 0.3 0.55 0.05 a. Determine the probability of the condition of the soil to be poor next year, it b. Determine the probability of the condition of the soil to be good in the next c. Determine the probability of the condition of the soil to fair in the next two now is fair. two years if now the condition of the soil is poor. years, if now the condition of the soil is fair.

Explanation / Answer

(a)

Transition probability form 'Fair' to 'Poor' is 0.30 from the table.

So, the probability of the condition to be poor next year if now is fair = 0.30

(b)

Define pijn = transition probability from state i to j where (i, j) = 1,2,3 and Good=1, Fair=2, and Poor=3 and 'n' stands for the number of times the transition is carried out.

We have to find p312

p312 = p31.p11 + p32.p21 + p33.p31 = 0.05*0.30 + 0.40*0.10 + 0.55*0.05 = 0.0825

(c)

Here, We have to find p222

p222 = p21.p12 + p22.p22 + p23.p32 = 0.10*0.60 + 0.60*0.60 + 0.30*0.40 = 0.54

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.