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Question 1 Alice is suffering from bipolar disorder, i.e. she experiences random mood swings between emotional highs (mania) and lows (depresssion). If she has her emotional high chances are that she = 0.8 or that she will become depressive with will stay in this manic state with probability p probability p= 0.2. However, if she is despressive, chances are that she will remain depressive with probability p = 0.35 or that she will make a recovery and switch to another emotional and energetic high with probability p= 0.65. a. Draw the graphical representation of this Markov chain. b. Is this Markov chain absorbing? c. Find the equilibrium distribution of this Markov chain. That is, on how many days can we expect Alice to be either manic or depressive on average?

Question 1 Alice is suffering from bipolar disorder, i.e. she experiences random mood swings between emotional highs (mania) and lows (depresssion). If she has her emotional high chances are that she = 0.8 or that she will become depressive with will stay in this manic state with probability p probability p= 0.2. However, if she is despressive, chances are that she will remain depressive with probability p = 0.35 or that she will make a recovery and switch to another emotional and energetic high with probability p= 0.65. a. Draw the graphical representation of this Markov chain. b. Is this Markov chain absorbing? c. Find the equilibrium distribution of this Markov chain. That is, on how many days can we expect Alice to be either manic or depressive on average?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question 1 Alice is suffering from bipolar disorder, i.e. she experiences random mood swings between emotional highs (mania) and lows (depresssion). If she has her emotional high chances are that she will stay in this manic state with probability p = 0.8 or that she will become depressive with probability p = 0.2. However, if she is despressive, chances are that she will remain depressive with probability p= 0.35 or that she will make a recovery and switch to another emotional and energetic high with probability p= 0.65. a. Draw the graphical representation of this Markov chain. b. Is this Markov chain absorbing? c. Find the equilibrium distribution of this Markov chain. That is, on how many days can we expect Alice to be either manic or depressive on average?
Transcribed Image Text:Question 1 Alice is suffering from bipolar disorder, i.e. she experiences random mood swings between emotional highs (mania) and lows (depresssion). If she has her emotional high chances are that she will stay in this manic state with probability p = 0.8 or that she will become depressive with probability p = 0.2. However, if she is despressive, chances are that she will remain depressive with probability p= 0.35 or that she will make a recovery and switch to another emotional and energetic high with probability p= 0.65. a. Draw the graphical representation of this Markov chain. b. Is this Markov chain absorbing? c. Find the equilibrium distribution of this Markov chain. That is, on how many days can we expect Alice to be either manic or depressive on average?
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