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#276 2013-04-01 04:25:07

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,480

Re: Expectation

Correct a Mundo! One of the cornerstones of experimental mathematics.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#277 2013-04-01 04:26:03

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,364

Re: Expectation

It seems the the denominator is always a power of the number of bins, as expected.


“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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#278 2013-04-01 04:27:27

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,480

Re: Expectation

Now you only have to work on the numerators. And they are integers.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#279 2013-04-01 04:31:15

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,364

Re: Expectation

But, some of the numerator might have to be multiplied by a factor.


“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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#280 2013-04-01 04:34:03

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,480

Re: Expectation

Why do you say that?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#281 2013-04-01 04:36:16

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,364

Re: Expectation

Because it might be lost when the denominator and the numerator are canceled.


“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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#282 2013-04-01 04:39:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,480

Re: Expectation

Very good, you are correct.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#283 2013-04-01 04:41:18

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,364

Re: Expectation

But, it is hard to figure out what the factor is for each of those fractions... What do we do now?


“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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#284 2013-04-01 04:43:23

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,480

Re: Expectation

If you know that the denominators were powers of 3, you should be able to reconstruct the numerators.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#285 2013-04-01 04:51:41

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,364

Re: Expectation

But, the trouble is that for 3 bins and 5 balls needed, the denominator is greater than 3^4...


“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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#286 2013-04-01 04:56:10

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,480

Re: Expectation

It seems that cancellation is not the problem. 9^3, 9^7 ... is gone!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#287 2013-04-01 05:07:01

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,364

Re: Expectation

I think the denominators have to form the series 3^(3*(k-1)).


“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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#288 2013-04-01 05:11:08

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,480

Re: Expectation

Hi;

Not every sequence has a general term that is expressible in terms of elementary functions.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#289 2013-04-01 05:17:07

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,364

Re: Expectation

I am sure the denominators have to be of the form 3^(3*(k-1)).


“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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#290 2013-04-01 05:23:41

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,480

Re: Expectation

That produces this table:

{1,27,729,19683,531441,...}

the denominators look like this:

You can see what was cancelled from each one and put it back.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#291 2013-04-01 05:32:03

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,364

Re: Expectation

Yes. So, the factors we need to multiply the numerator by are {1,3,9,3,9}.


“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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#292 2013-04-01 05:36:55

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,480

Re: Expectation

You could try that. Try to read as much of the help as you can for the next couple of days.

I am going offline, I have to pay bills.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#293 2013-04-01 05:39:15

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,364

Re: Expectation

Okay, see you later!


“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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#294 2013-04-01 08:16:17

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,480

Re: Expectation

Had to pay some bills and the rent.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#295 2013-04-01 08:29:29

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,364

Re: Expectation

Okay. OEIS has nothing on our numerator sequence...


“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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#296 2013-04-01 08:34:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,480

Re: Expectation

How about going across instead of down?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#297 2013-04-01 09:07:59

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,364

Re: Expectation

I haven't tried. I will tomorrow, because I am watching Doctor Who now.


“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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#298 2013-04-01 09:14:30

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,480

Re: Expectation

Okay that is fine, I am going to get some sleep.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#299 2013-04-01 09:23:14

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,364

Re: Expectation

Okay, see you later!


“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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#300 2013-04-01 15:42:25

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,480

Re: Expectation

Okay. OEIS has nothing on our numerator sequence...

Even after you adjusted the numerators for the missing 3's?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

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