An ant stays at one corner of a cube. It can go only along the side with
equal probability, and taking one minute to get to another corner. What is
the expect minutes for the ant coming back to the original position?
can you give some more elaboration of that problem becoz i think some
condition will be der. whether max time, min time avg time ...... like of
ant can traverse each once like that........
On Tue, Nov 3, 2009 at 9:44 AM, ankur aggarwal <ankur.mast....@gmail.com>wrote:
> An ant stays at one corner of a cube. It can go only along the side with
> equal probability, and taking one minute to get to another corner. What is
> the expect minutes for the ant coming back to the original position?
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Define L1 as being a hop away from the origin, L2 as being 2 hops away
from origin, L3 as being 3 hops away.
Thus we are looking for E[X|L1] since originally the ant is only a hop
away.
So, E[X|L1]=1/3(1)+2/3(E[X|L2]+1) since it may return to the origin
with chance 1/3 or go away another level with chance 2/3
Then, E[X|L2]=2/3(E[X|L1]+1)+1/3(E[X|L3]+1) since it may get closer
with chance 2/3, or further.
Finally, E[X|L3]=E[X|L2]+1 since it has no choice but to get closer.
Hence, E[X|L2]=2/3(E[X|L1]+1)+1/3(E[X|L2]+2) => 2/3(E[X|L2])=2/3(E[X|
L1]+1)+2/3=>E[X|L2]=E[X|L1]+2
Thus, E[X|L1]=1/3(1)+2/3(E[X|L1]+3)=> E[X|L1]=7
On Nov 2, 11:14 pm, ankur aggarwal <ankur.mast....@gmail.com> wrote:
> An ant stays at one corner of a cube. It can go only along the side with
> equal probability, and taking one minute to get to another corner. What is
> the expect minutes for the ant coming back to the original position?
> An ant stays at one corner of a cube. It can go only along the side with
> equal probability, and taking one minute to get to another corner. What is
> the expect minutes for the ant coming back to the original position?
On Nov 2, 11:14 pm, ankur aggarwal <ankur.mast....@gmail.com> wrote:
> An ant stays at one corner of a cube. It can go only along the side with
> equal probability, and taking one minute to get to another corner. What is
> the expect minutes for the ant coming back to the original position?
> On Nov 2, 11:14 pm, ankur aggarwal <ankur.mast....@gmail.com> wrote:
> > An ant stays at one corner of a cube. It can go only along the side with
> > equal probability, and taking one minute to get to another corner. What
> is
> > the expect minutes for the ant coming back to the original position?
> Eight minutes.
> --
> Geoff
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-- We are here on earth to do good for others. What the others are here for, I
don't know.
Afroz Mohiuddin
Final Year Masters Student
Dept Computer Science and Engineering
Indian Institute of Technology Kanpur
Kanpur - 208016
INDIA
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On Nov 6, 11:08 am, ankur aggarwal <ankur.mast....@gmail.com> wrote:
> @geoffery
> plz give your method..
Simple enough, xe's analysis is correct,
except xe starts at L1. The ant starts at
the origin and moves to L1 with a probability
of 1, accounting for one extra minute.
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