The President of the United States tells person A his or her intention to run or

Question

The President of the United States tells person A his or her intention to run or not to run in the next election. Then A relays the news to B, who in turn relays the message to C, and so forth, always to some new person. We assume that there is a 40% probability that a person will change the answer from yes to no when transmitting it to the next person and a 30% probability that he or she will change it from no to yes. We choose as states the message ''either yes or no. The transition matrix is then yes no P = yes 0.6 0.4 no 0.3 0.7 If the president's choice is "yes" then what is the probability that the third person to get the message gets the correct choice? If the president's choice is "no" then what is the probability that the second person to get the message gets the incorrect choice? Is this an ergo die Markov chain?

Explanation / Answer

c) Yes it is a ergodic Markov Chain because it is a chain in which we can move from every state to every state it is also called irreducible.

We have Transition matrix as P= for no

                                             = 1-P(yes)

                                             = 1-(0.6)

                                            = 0.94

                                            

For the choice of yes = 1-P(no)

                                      1-(0.12 +0.21)

                                    =1- (0.33)

                                     = 0.77

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