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# halps plssss asapp

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Anty the ant is on the real number line, and Anty's goal is to get to \$0.\$ If Anty is at \$1,\$ then on the next step, Anty moves to either \$0\$ or \$2\$ with equal probability. If Anty is at \$2,\$ then on the next step, Anty always moves to \$1.\$ Let \$e_1\$ be expected number of steps Anty takes to get to \$0,\$ given that Anty starts at the point \$1.\$ Similarly, let \$e_2\$ be expected number of steps Anty takes to get to \$0,\$ given that Anty starts at the point \$2.\$ Determine the ordered pair \$(e_1,e_2)\$.

Feb 14, 2020

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You can track the probabilities using different case, i.e. Anty gets to 0 after 1 steps, 2 steps, 3 steps, and so on.  This gives us e_1 = 1/2*1 + 1/4*2 + 1/8*3 + 1/16*4 + ... By arithmetico-geometric series, e_1 = 2.  Similarly, e_2 = 1/2*2 + 1/4*3 + 1/8*4 + 1/16*5 + ... = 3, so (e_1,e_2) = (2,3).

Feb 14, 2020
#3
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i tried that... its incorrect :(

Guest Feb 14, 2020
#2
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Here: https://web2.0calc.com/questions/help_88352

Feb 14, 2020
#4
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thank you so much!

Guest Feb 14, 2020