Thread: Transition Matrix question

a housekeeper buys three kinds of cereal; A,B,C. She never buys the same cereal in successive weeks. if she buys cereal A, then the next week she buys cereal B. However, if she buys either B or C, then the next week she is three times as likely to buy A as the other brand.

a) find the transition matrix
b) in the long run, how often does she buy each of the three brands?


for a. i got
T=
[0 1 0]
|.6 0 .2|
[.6 .2 0]

im not sure how to do the second part or if i got the right transition matrix for part a. help?

I think the matrix should be:



Isn't then an initial-state matrix needed to calculate the rest?

Anyway, if you have an initial state matrix, called and then the transition matrix above, called , the first state matrix, would be calculated as follows: . The second state matrix as: . The k-th state matrix:

I'm not quite sure about those Markov chains, but I hope that helps.

Originally Posted by jellosalade

a housekeeper buys three kinds of cereal; A,B,C. She never buys the same cereal in successive weeks. if she buys cereal A, then the next week she buys cereal B. However, if she buys either B or C, then the next week she is three times as likely to buy A as the other brand.

a) find the transition matrix
b) in the long run, how often does she buy each of the three brands?


for a. i got
T=
[0 1 0]
|.6 0 .2|
[.6 .2 0]

im not sure how to do the second part or if i got the right transition matrix for part a. help?

Asked here: http://www.mathhelpforum.com/math-he...on-matrix.html

Thread closed.