Question

At a particular farmers market, they sell three kinds of fruit: strawberry, cherries, and blueberries. Assume that the farmers market has only one customer at a time. The owner estimates that strawberries are 50% likely to be followed by more strawberries, 15% likely to be followed by blueberries, and 35% likely to be followed by cherries. He also estimates that cherries are 45% likely to be followed by more cherries, 35% likely to be followed by strawberries, and 20% likely to be followed by blueberries. Lastly, he believes that blueberries are followed by more blueberries 45% of the time, and that strawberries are 25% likely to follow blueberries. For this problem, assume that the owner's estimated probabilities are exactly correct.

a) Draw a three state Markov chain for this problem

b) Create the transition matrix

c) Find the stationary distribution

d) Find the limit distribution

e) About what percentage bought will be strawberries, in the long run?

f) If the first fruit bought is strawberries, what is the probability that the 10th fruit bought is also strawberries?

g) If the first fruit bought is strawberries, what is the probability that the first 10 fruits bought will all be strawberries?

Answer 1