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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,258

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

gAr
Member
Registered: 2011-01-09
Posts: 3,479

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: 87,258

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

gAr
Member
Registered: 2011-01-09
Posts: 3,479

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: 87,258

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

gAr
Member
Registered: 2011-01-09
Posts: 3,479

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: 87,258

Re: rat run probability

Hi gAr;

Thanks for providing that!


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

gAr
Member
Registered: 2011-01-09
Posts: 3,479

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: 87,258

Re: rat run probability

Hi gAr;

Thanks for the pdf.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,181
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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,258

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#137 2014-09-09 02:23:20

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,181
Website

Re: rat run probability

bobbym wrote:

Hi;

Two ways, computer simulation and Absorbing Markov chain. There is a third way but I am unable to get it to work,

Please post the markov chain solution


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#138 2014-09-09 02:29:17

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,258

Re: rat run probability

Where does the rat start and where does it end?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#139 2014-09-09 02:33:26

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,181
Website

Re: rat run probability

1,3


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#140 2014-09-09 02:35:55

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,258

Re: rat run probability

In the original problem he ends up in the space to leave room 3.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#141 2014-09-09 02:37:31

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,181
Website

Re: rat run probability

I am sorry. Will you please absorbing chains with the standard drunkyard example?


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#142 2014-09-09 02:48:31

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,258

Re: rat run probability

A man walks along a four block stretch of Park Avenue.If he is at corner 1,2,or 3, then he walks to the left or right
with equal probability. He continues until he reaches corner 4, which is a bar, or corner 0, which is his home.

If he reaches either home or the bar, he stays there.

Is this okay?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#143 2014-09-09 02:49:51

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,181
Website

Re: rat run probability

They say that the absorption probability matrix is B=NR but I do not get it.


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#144 2014-09-09 02:50:31

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,258

Re: rat run probability

One thing at a time, is the problem acceptable?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#145 2014-09-09 02:51:58

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,181
Website

Re: rat run probability

Sorry, I missed that post.

Where does the man start from?

Last edited by Agnishom (2014-09-09 02:52:48)


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#146 2014-09-09 03:01:51

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,258

Re: rat run probability

He starts in state 2. Do you have a simulation answer available?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#147 2014-09-09 03:08:42

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,181
Website

Re: rat run probability

No, but I know the answer to the question is half.

Please continue explaining and thank you.


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#148 2014-09-09 03:16:36

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,258

Re: rat run probability

P2 = DiscreteMarkovProcess[3, A];
PDF[P2[\[Infinity]], 1]
PDF[P2[\[Infinity]], 5]

In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#149 2014-09-09 03:25:40

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,181
Website

Re: rat run probability

Pdf?


'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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#150 2014-09-09 03:26:46

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,258

Re: rat run probability

Please continue in the thread I have created for this problem.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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