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Fred the ant is on the real number line, and Fred is trying to get to the point 0.

 

If Fred is at 1, then on the next step, Fred moves to either 0 or 2 with equal probability. If Fred is at 2, then on the next step, Fred always moves to 1. Let e_1 be expected number of steps Fred takes to get to 0, given that Fred starts at the point 1. 

 

Similarly, let e_2 be expected number of steps Fred takes to get to 0, given that Fred starts at the point 2. Determine the ordered pair (e_1,e_2).

 Jul 15, 2020
edited by Guest  Jul 15, 2020
 #1
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You can use the state diagram approach for these kinds of problems.  This gives you (e_1,e_2) = (2,4).


Reference: http://www.aquatutoring.org/ExpectedValueMarkovChains.pdf

 Jul 15, 2020
 #2
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I am so sorry it is incorrect.

Guest Jul 15, 2020

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