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#126 2013-04-04 06:58:36

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,748

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.

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#127 2013-04-04 17:51:25

gAr
Member
Registered: 2011-01-09
Posts: 3,462

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."

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#128 2013-04-04 19:25:18

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,748

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.

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#129 2013-04-04 19:45:34

gAr
Member
Registered: 2011-01-09
Posts: 3,462

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."

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#130 2013-04-04 19:55:20

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,748

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.

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#131 2013-04-04 20:51:52

gAr
Member
Registered: 2011-01-09
Posts: 3,462

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."

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#132 2013-04-04 20:57:57

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,748

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.

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#133 2013-04-04 21:17:50

gAr
Member
Registered: 2011-01-09
Posts: 3,462

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 (2013-04-04 21:51:40)


"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."

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#134 2013-04-04 23:10:23

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,748

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.

Offline

#135 2013-04-05 02:16:36

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,390
Website

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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#136 2013-04-05 02:22:39

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,748

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.

Offline

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