Math Is Fun Forum
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#126 2013-04-04 06:58:36
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#127 2013-04-04 17:51:25
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
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
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#129 2013-04-04 19:45:34
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
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
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#131 2013-04-04 20:51:52
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
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
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: rat run probability
Hi gAr;
Thanks for providing that!
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#133 2013-04-04 21:17:50
- gAr
- Member
- Registered: 2011-01-09
- Posts: 3,482
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
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: rat run probability
Hi gAr;
Thanks for the pdf.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#135 2013-04-05 02:16:36
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'
I'm not crazy, my mother had me tested.
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#136 2013-04-05 02:22:39
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#137 2014-09-09 02:23:20
Re: rat run probability
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'
I'm not crazy, my mother had me tested.
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#138 2014-09-09 02:29:17
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#139 2014-09-09 02:33:26
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'
I'm not crazy, my mother had me tested.
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#140 2014-09-09 02:35:55
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#141 2014-09-09 02:37:31
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'
I'm not crazy, my mother had me tested.
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#142 2014-09-09 02:48:31
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#143 2014-09-09 02:49:51
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'
I'm not crazy, my mother had me tested.
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#144 2014-09-09 02:50:31
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#145 2014-09-09 02:51:58
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'
I'm not crazy, my mother had me tested.
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#146 2014-09-09 03:01:51
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#147 2014-09-09 03:08:42
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'
I'm not crazy, my mother had me tested.
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#148 2014-09-09 03:16:36
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#149 2014-09-09 03:25:40
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'
I'm not crazy, my mother had me tested.
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#150 2014-09-09 03:26:46
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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