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#126 2013-04-05 05:58:36

bobbym
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Re: rat run probability

Hi gAr;

Yes, it did but the trouble was with the denominator I chose. anonimnystefy used bayes theorem to choose the right one.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#127 2013-04-05 16:51:25

gAr
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Re: rat run probability

Hi,

The simulations match closely with the answers for (ii) and (iii), so I believe they are right.


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

#128 2013-04-05 18:25:18

bobbym
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Re: rat run probability

Hi;

That is what I am getting too.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#129 2013-04-05 18:45:34

gAr
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Re: rat run probability

Hi bobbym,

Thanks for confirming.


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

#130 2013-04-05 18:55:20

bobbym
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Re: rat run probability

I am having trouble getting the exact answer though. How did you get it?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#131 2013-04-05 19:51:52

gAr
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Re: rat run probability

Hi,

I derived the probabilities for (iii) from the matrix
           st                1                2                3          end1        end23
st         0 0.7000000 0.2000000 0.1000000 0.0000000 0.0000000
1          0 0.0000000 0.5000000 0.0000000 0.5000000 0.0000000
2          0 0.3333333 0.0000000 0.3333333 0.3333333 0.0000000
3          0 0.0000000 0.3333333 0.0000000 0.0000000 0.6666667
end1    0 0.0000000 0.0000000 0.0000000 1.0000000 0.0000000
end23  0 0.0000000 0.0000000 0.0000000 0.0000000 1.0000000

and used bayes' rule


1_s means starts at first room, 1_e means exits from first room

You need to slightly change the matrix for P(1_e|1_s) by changing .7 to 1 and rest in that row to zeroes.


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

#132 2013-04-05 19:57:57

bobbym
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Re: rat run probability

Hi gAr;

Thanks for providing that!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#133 2013-04-05 20:17:50

gAr
Star Member

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Re: rat run probability

You're welcome!
Found a pdf which solved for the expected number of steps for the rat to exit from the maze : http://www.columbia.edu/~ks20/stochasti … -I-MCI.pdf

Last edited by gAr (2013-04-05 20:51:40)


"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

#134 2013-04-05 22:10:23

bobbym
Administrator

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Re: rat run probability

Hi gAr;

Thanks for the pdf.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#135 2013-04-06 01:16:36

Agnishom
Real Member
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Re: rat run probability

May I post another problem of Bayes' theorem?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Who are you to judge everything?' -Alokananda

#136 2013-04-06 01:22:39

bobbym
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Re: rat run probability

Might be better to post it in a new thread.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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