A study of pine nut crops in the American southwest from 1940 to 1947 hypothised that nut production followed a Markov chain. The data suggested that if one year's crop was good, then the probabilities that the following year's crop would be good, fair, or poor were 0.08, 0.07, and 0.85, respectively; if one year's crop was fair, then the probabilities that the follow-ing year's crop would be good, fair, or poor were 0.09, 0.11, and 0.80, respectively; if one year's crop was poor, then the probabilities that the following year's crop would be good, fair, or poor were 0.11, 0.05, and 0.84, respectively. (a) Write down the transition matrix for this Markov chain. (b) If the pine nut crop was good in 1940, find the probabilities of a good crop in the years 1941 through 1945. (c) In the long run, what proportion of the crops will be good, fair, and poor
A study of pine nut crops in the American southwest from 1940 to 1947 hypothised that nut production followed a Markov chain. The data suggested that if one year's crop was good, then the probabilities that the following year's crop would be good, fair, or poor were 0.08, 0.07, and 0.85, respectively; if one year's crop was fair, then the probabilities that the follow-ing year's crop would be good, fair, or poor were 0.09, 0.11, and 0.80, respectively; if one year's crop was poor, then the probabilities that the following year's crop would be good, fair, or poor were 0.11, 0.05, and 0.84, respectively. (a) Write down the transition matrix for this Markov chain. (b) If the pine nut crop was good in 1940, find the probabilities of a good crop in the years 1941 through 1945. (c) In the long run, what proportion of the crops will be good, fair, and poor
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 7 images
