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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 \((e_1, e_2)\).

 

Answer is not 2,3 or 2,4

 Jun 19, 2020
 #1
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(e_1,e_2) works out to (4,6).

 Jun 19, 2020

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