Reference no: EM132372725
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 probability a that a person will change the answer from yes to no when transmitting it to the next person and a probability b that he or she will change it from no to yes. We choose as states the message, either yes or no. The transition probabilities are
Pyes,no = a, Pno,yes = b
The initial state represents the President's choice. Suppose a = 0.5,b = 0.75.
(a) Assume that the President says that he or she will run. Find the expected length of time before the ?rst time that the answer is passed on incorrectly.
(b) Find the mean recurrence time for each state. In other words, ?nd the expected amount of time ri, for i = yes and i = no required to return to that state.
(c) Write down the transition probability matrix P and ?nd limn→∞P^n.
(d) Repeat (b) for general a and b.
(e) Repeat (c) for general a and b.
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