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#226 2013-03-21 02:26:45

bobbym
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Re: Expectation

For me it always was one of the best.


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.
 

#227 2013-04-01 23:53:13

anonimnystefy
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Re: Expectation

Is there a pattern in these?

Last edited by anonimnystefy (2013-04-01 23:53:28)


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#228 2013-04-02 00:07:12

bobbym
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Re: Expectation

Up - down or left - right?


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.
 

#229 2013-04-02 00:08:15

anonimnystefy
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Re: Expectation

Both.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#230 2013-04-02 00:09:05

bobbym
Administrator

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Re: Expectation

How about the first column, can you supply more?


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.
 

#231 2013-04-02 00:10:21

anonimnystefy
Real Member

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Re: Expectation

11, 12, 13, 14, 15...


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#232 2013-04-02 00:12:00

bobbym
Administrator

Online

Re: Expectation

Hi;

Yes, the more the merrier!


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.
 

#233 2013-04-02 00:14:54

anonimnystefy
Real Member

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Re: Expectation

Well, the first column is obvious. Those are the natural numbers...


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#234 2013-04-02 00:28:13

bobbym
Administrator

Online

Re: Expectation

Yikes! That is a good one. The second column.


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.
 

#235 2013-04-02 00:30:51

anonimnystefy
Real Member

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Re: Expectation

You can generate all the numbers you need:

Code:

f[bins_, k_] := Sum[i*(i - k)!/(bins^(i - 1))*Binomial[i - 1, k - 1]*Coefficient[(Sum[x^j/j!, {j, 0, k - 1}])^(bins - 1), x, i - k], {i,k, bins*(k - 1) + 1}]
MatrixForm[Table[Table[f[i, j], {i, 1, 10}], {j, 1, 10}]]

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#236 2013-04-02 00:36:25

bobbym
Administrator

Online

Re: Expectation

Hmmm, that looks like M code to me.


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.
 

#237 2013-04-02 00:45:02

anonimnystefy
Real Member

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Re: Expectation

It is M code.

And the function f is the function which calculates the expected value for k balls to appear in a bin, where the number of bins is represented bt the number "bins".


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#238 2013-04-02 00:51:48

bobbym
Administrator

Online

Re: Expectation

Are you aware of its awesome firepower?


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.
 

#239 2013-04-02 01:03:10

anonimnystefy
Real Member

Offline

Re: Expectation

Like what?


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#240 2013-04-02 01:04:33

bobbym
Administrator

Online

Re: Expectation

FindSequenceFunction for one thing...


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.
 

#241 2013-04-02 01:08:37

anonimnystefy
Real Member

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Re: Expectation

I got this for 2 bins:


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#242 2013-04-02 01:16:01

bobbym
Administrator

Online

Re: Expectation

You mean:


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.
 

#243 2013-04-02 01:16:51

anonimnystefy
Real Member

Offline

Re: Expectation

Well, it spit out the above for me...


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#244 2013-04-02 01:18:14

bobbym
Administrator

Online

Re: Expectation

If it spits at you then you have to beat it into submission until it gives that answer.


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.
 

#245 2013-04-02 01:19:45

anonimnystefy
Real Member

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Re: Expectation

How did you get that answer?

I entered:

Code:

FindSequenceFunction[Table[f[2, j], {j, 1, 100}]]

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#246 2013-04-02 01:23:37

bobbym
Administrator

Online

Re: Expectation

Underneath any answer should be the command bar.


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.
 

#247 2013-04-02 01:27:38

anonimnystefy
Real Member

Offline

Re: Expectation

There is. I have plot, evaluate at a point, differentiate and integrate...


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#248 2013-04-02 01:32:04

bobbym
Administrator

Online

Re: Expectation

You have more there than I do. But it changes, trying to figure what you want.

After you compute your answer, type in a new cell

FullSimplify[%]


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.
 

#249 2013-04-02 01:34:22

anonimnystefy
Real Member

Offline

Re: Expectation

It's still the same...

What did you enter, exactly?


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#250 2013-04-02 01:37:08

bobbym
Administrator

Online

Re: Expectation

First take the MatrixForm wrapper off the original code and change it to this:

ans=Table[Table[f[i,j],{i,2,2}],{j,1,15}]


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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