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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

Be sure to tell if you get an idea!

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,339

I have something. It will take some time.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

Can you post just the beginning steps?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,339

Calculation is running, it will take a while.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

Post when it's done.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,339

Hi;

Procedure failed, I do not know why.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

What procedure?

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,339

An attempt to develope an asymptotic form that would have eliminated the coefficient part of your maxima code.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

Can you elaborate?

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,339

Instead of picking out the i - k power of x out of the expansion. For large k, I figured that expansion would approach (e^x)^5. The coefficient of x^(i-k) of that is 5^(i-k) / (i-k)!. For large k this would have replaced expanding a big polynomial raised to the 5th power. Unfortunately, it did not work.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

Why not?

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,339

I do not know. I tested it for k = 20, 30 , 40 , 50, 60, 100, 200. It did not asymptotically approach the exact answer.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

I guess that there are too many terms that contribute to the x^(i-k) term.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,339

I am not sure, I will think about it.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

Hi bobbym

I got a reply. He said he does not need the solution if it just involves the standard bunch of methods.

Personally, I really do not think that that problem is the best one for showing how Markov chains can be used, but, it is his work, and I will not insist on it anymore.

I would still like to continue working on an analityc form here.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,339

Personally, I really do not think that that problem is the best one for showing how Markov chains can be used, but, it is his work, and I will not insist on it anymore.

I am not following you. He does not always use Markov chains. Your method is a standard method, even though I do not know what he means by that.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

Hi bobbym

What I meant to say is, if he wanted to show how Markov chains work, he should've done it on a smaller and bit simpler problem.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,339

Hi;

I am not suggesting that you persist in publishing. That is a decision that is up to you, but the purpose of that pdf is not to just demonstrate Markov chains. It is to solve dice problems.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

Again you misunderstood me. He said that, if the answer is a classical one, then he doesn't need it. He obviously wants the second part of 10th problem to be with Markov chains.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,339

That is impossible, the next one would require a 4097 x 4097 matrix!

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

I meant for the 3 case.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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

Hi bobbym,

I think we can't approximate it using e^(5x), since we are using coefficients beyond the upper limit of the egf. Below is the probability plot for n=45.

Hi anonimnystefy,

Standard bunch of methods? Did he mean he has solution for that already, but did not publish in his pdf?

*Last edited by gAr (2013-02-17 21:35:14)*

"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: 104,339

He already solved the 3 case. It took a 730 x 730 matrix. He will never get a general answer as you did using Markov chains.

*Last edited by bobbym (2013-02-17 21:35:33)*

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

bobbym wrote:

He already solved the 3 case. It took a 730 x 730 matrix. He will never get a general answer as you did using Markov chains.

Yes, but it seems he wanted to show how Markov chains work on particularly that problem.

Anyway, there is no point in discussing it any more. Have you found anything else that could help us with the GF?

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,339

Hi;

I am not unhappy with your decision, as I said it is your choice. You should be advised though that someone from another forum will eventually see your solution, change it a bit and call it his own.

I could possibly shorten the computation a bit but I do not want to do that. I would prefer to eliminate the gf or to just leave it as it is.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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