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?

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter12: Probability

Section12.3: Conditional Probability; Independent Events; Bayes' Theorem

Problem 42E

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