+0  
 
0
44
3
avatar

Max the ant is on the real number line, and Max is trying to get to the point \(0\).

If Max is at \(1\), then on the next step, Max moves to either \(0\) or \(2\) with equal probability. If Max is at \(2\), then on the next step, Max always moves to \(1\).

Let \(e_1\) be expected number of steps Max takes to get to \(0\), given that Max starts at the point \(1\). Similarly, let \(e_2\) be expected number of steps Max takes to get to \(0\) given that Max starts at the point \(2\).

Determine the ordered pair \((e_1,e_2)\).

 May 2, 2020
 #1
avatar+657 
0

Repost? - "https://web2.0calc.com/questions/anty-the-ant-is-on-the-real-number-line-and-anty"

 

coolsmileycool

 May 2, 2020
 #2
avatar
0

The answers there are wrong!

Guest May 2, 2020
 #3
avatar+30046 
+3

e1:

 

E(steps) = 1*(1/2) + 3*(1/22) + 5*(1/23) + ... + (2n-1)*(1/2n) + ...

 

E(steps) = Sumn=1 to inf( (2n-1)/2n ) = 2

 

e2:

 

E(steps) = 2*(1/2) + 4*(1/22) + 6*(1/23) + ... + 2n*(1/2n) + ...

 

E(steps) = Sumn=1 to inf(2n/2n) = 4

 

(e1, e2) = (2, 4)

 May 2, 2020

21 Online Users

avatar