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#26 2013-07-29 00:43:35

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,676

Re: Probability problem.

Have you ever seen anonimnystefy's problem that he posed a while back?


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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#27 2013-07-29 00:45:24

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

Re: Probability problem.

Which problem is that?


"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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#28 2013-07-29 00:48:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,676

Re: Probability problem.

http://www.mathisfunforum.com/viewtopic … 00#p243200

Any ideas since then?

See you a little later, chore came up.


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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#29 2013-07-29 01:54:10

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

Re: Probability problem.

Hi bobbym,

I did not spend much time on the problem after that, let me see whether I can get anything else this time.


"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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#30 2013-07-29 04:42:51

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,676

Re: Probability problem.

Hi gAr;

Okay, thanks I am looking at it also.


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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#31 2013-07-29 13:55:10

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,525

Re: Probability problem.

looks like a nice upper bound to start with.

Last edited by anonimnystefy (2013-07-29 13:55:32)


“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

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#32 2013-07-29 15:33:56

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,676

Re: Probability problem.

Hi;

Upper and lower bounds imply some method of getting them. How?


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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#33 2013-07-30 18:21:06

ElainaVW
Member
Registered: 2013-04-29
Posts: 291

Re: Probability problem.

Hello,

gAr and bobbym those are the correct answers.

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#34 2013-07-30 18:26:25

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,676

Re: Probability problem.

Hi;

Thanks for the 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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#35 2013-09-23 03:11:29

ElainaVW
Member
Registered: 2013-04-29
Posts: 291

Re: Probability problem.

Hello:

How many Lucky Numbers are there and show 3 ways to find them? smile

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#36 2013-09-23 03:16:04

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,676

Re: Probability problem.

Hi;


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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#37 2013-09-25 05:16:22

ElainaVW
Member
Registered: 2013-04-29
Posts: 291

Re: Probability problem.

Hello m:

I could use a bit of help on some M code. smile

Why do you call it Spasmatica?

Where does the integral come from? How can I evaluate it to many digits?

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#38 2013-09-25 05:21:41

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,676

Re: Probability problem.

I do not always call it that. Sometimes it is Asthmatica as well as some more colorful names.

Everything came from the Lando lectures.


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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#39 2013-09-25 05:24:30

ElainaVW
Member
Registered: 2013-04-29
Posts: 291

Re: Probability problem.

What are the Lando lectures?

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#40 2013-09-25 05:26:41

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,676

Re: Probability problem.

Lectures on Generating Functions by Lando, it is a book. I thought you had read 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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#41 2013-09-25 05:29:04

ElainaVW
Member
Registered: 2013-04-29
Posts: 291

Re: Probability problem.

I have that one. smile

How do you get the integral to say a hundred digits?

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#42 2013-09-25 05:34:15

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,676

Re: Probability problem.

I have that one.

Yes I know. I gave it to you. You might try reading it.

M can handle the integral exactly. You do not need an approximate answer.


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.

Offline

#43 2013-09-25 05:56:09

ElainaVW
Member
Registered: 2013-04-29
Posts: 291

Re: Probability problem.

Oooh yes, I am sorry. It didn't work for me at first. The integral comes from complex analysis? From getting a0 of the Laurent series?

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#44 2013-09-25 05:56:11

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

Re: Probability problem.

Hi,

I was thinking about the integral you wrote there, I had

I got the first two answers using the g.f


"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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#45 2013-09-25 06:05:17

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,676

Re: Probability problem.

It is straight out of the book. It does get the right answer. The derivation is a bit too tough for me.

What did you think of the NCR answer?


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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#46 2013-09-25 06:23:45

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

Re: Probability problem.

nCr answer is derived from the g.f:
[z^27] in


"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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#47 2013-09-25 06:28:13

ElainaVW
Member
Registered: 2013-04-29
Posts: 291

Re: Probability problem.

Hello gAr;

That is good but it can also be derived from the principle of inclusion and exclusion.

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#48 2013-09-25 06:29:20

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,676

Re: Probability problem.

Hi;

I can follow gAr's better than that stuff on PIE. Did you understand 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.

Offline

#49 2013-09-25 06:36:03

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

Re: Probability problem.

Hi ElainaVW,

I usually get PIE answers wrong, so I try to stay away from it!
When it's the case that g.f. is possible, I go for that.


"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

#50 2013-09-25 07:05:44

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,676

Re: Probability problem.

That is the way I feel about it too. I have a done a few of them but prefer generating functions.


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.

Offline

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