1. Abigail spends her entire weekly allowance on either candy or toys. If she buys candy one week, she is 60% sure to buy toys the next week. The probability that she buys toys in two successive weeks is 25%. (a) Create a transition diagram that describes this scenario. (b) Create a transition matrix that describes this scenario. Is this scenario ergodic or absorbing? Explain. (c) Suppose that this week, Abigail spends all of her money (100%) on candy. Using matrix multiplication, predict the probability that Abigail buys toys or candy next week, the following week, and three weeks from now. (d) Find the eigenvalues and eigenvectors for this transition matrix. (e) In the long run, what is the probability that Abigail will spend her money on toys? Explain.

1. Abigail spends her entire weekly allowance on either candy or toys. If she buys candy one week, she is 60% sure to buy toys the next week. The probability that she buys toys in two successive weeks is 25%. (a) Create a transition diagram that describes this scenario. (b) Create a transition matrix that describes this scenario. Is this scenario ergodic or absorbing? Explain. (c) Suppose that this week, Abigail spends all of her money (100%) on candy. Using matrix multiplication, predict the probability that Abigail buys toys or candy next week, the following week, and three weeks from now. (d) Find the eigenvalues and eigenvectors for this transition matrix. (e) In the long run, what is the probability that Abigail will spend her money on toys? Explain.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.5: Markov Chain

Problem 47E: Explain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.

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