MAT 122 Lecture Notes - Lecture 17: Square Matrix
Document Summary
Trends show that from one month to the next, among brand 1- 80% of customers stay, 10% switch to brand 2, and 10% switch to brand 3. Brand 2- 20% switch to brand 1, 70% stay, and 10% switch to brand 3. Brand 3- 10% switch to brand 1, 30% switch to brand 2, and 60% stay: ways to organize this data, transition diagram. 6: transition matrix, in the ith row put the probabilities of going from state i to each of the other states. 1 . 3 . 6: p2 tells you two months in the future. 1 . 3 . 6 (. 8*. 8)+(. 1*. 2)+(. 1*. 1) (. 8*. 1)+(. 1*. 7)+(. 1*. 3) (. 8*. 1)+(. 1*. 1)+(. 1*. 6) (. 2*. 8)+(. 7*. 2)+(. 1*. 1) (. 2*. 1)+(. 7*. 7)+(. 1*. 3) (. 2*. 1)+(. 7*. 1)+(. 1*. 6) (. 1*. 8)+(. 3*. 2)+(. 6*. 1) (. 1*. 1)+(. 3*. 7)+(. 6*. 3) (. 1*. 1)+(. 3*. 1)+(. 6*. 6) 3 t e: pn tells you n months in the future, question, a customer buys brand 1 in june. What is the probability that they will buy brand 1 again: a customer buys brand 2 in june. Answer the questions (using the matrices from above) find the answer to question #1.
