Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,182

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.**

Offline

**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."

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,182

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.**

Offline

**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."

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,182

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.**

Offline

**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."

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,182

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.**

Offline

**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."

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,182

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.**

Offline

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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,182

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.**

Offline

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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,182

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.**

Offline

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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,182

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.**

Offline

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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,182

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.**

Offline

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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,182

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.**

Offline

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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,182

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.**

Offline

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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,182

```
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.**

Offline

Pdf?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 98,182

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.**

Offline