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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,364

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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,364

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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,364

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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,364

Hi gAr;

Thanks for providing that!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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

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)*

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,364

Hi gAr;

Thanks for the pdf.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,364

Might be better to post it in a new thread.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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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'

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,364

Where does the rat start and where does it end?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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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'

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,364

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,364

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?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,364

One thing at a time, is the problem acceptable?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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Sorry, I missed that post.

Where does the man start from?

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

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,364

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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

Please continue explaining and thank you.

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,364

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

`PDF[P2[\[Infinity]], 5]`

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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Pdf?

'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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,364

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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