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#26 2013-03-08 22:57:54

anonimnystefy
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Re: Simulations

Yes, I do.

By the way, I finally downloaded Acton's book.


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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

#27 2013-03-08 23:01:10

bobbym
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Re: Simulations

What took you so long with the book? He has another one too.

That is good work with the histogram. I need to do a chore I will be back in about a half hour.


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.

#28 2013-03-08 23:03:55

anonimnystefy
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Re: Simulations

Well, first I couldn't find a site that offers a *free* download. And then I forgot about searching.

Okay, see you then.


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

#29 2013-03-08 23:18:29

bobbym
Administrator

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Re: Simulations

Hi;

Okay, I got it. Lets start generating random numbers from non - uniform distributions!


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.

#30 2013-03-08 23:20:51

anonimnystefy
Real Member

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Re: Simulations

So, we need to transform a non-uniform into uniform ditributions, right?


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

#31 2013-03-08 23:21:46

bobbym
Administrator

Online

Re: Simulations

Nope, the other way. We are going to transform a uniform into another distribution.


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.

#32 2013-03-08 23:26:46

anonimnystefy
Real Member

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Re: Simulations

Okay, but how?


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

#33 2013-03-08 23:36:19

bobbym
Administrator

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Re: Simulations

We want to generate random numbers that are from the PDF f(x) = 2x from 0 to 1.



Solve the equation



for x. You get 2 solutions:



We take the positive one. Can you get maxima to do everything so far?


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.

#34 2013-03-08 23:52:55

anonimnystefy
Real Member

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Re: Simulations

Yes. Should I plot a histogram for sqrt(random(1.0))?


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

#35 2013-03-09 00:05:24

bobbym
Administrator

Online

Re: Simulations

Hi;

Correct! Get 10000 of them. You should get something like the picture. Notice how neatly our random numbers fit under y = 2x ( the red line ).


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View Image: 2013-03-08_045719.gif      


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.

#36 2013-03-09 00:11:07

anonimnystefy
Real Member

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Re: Simulations

Yup. Got it.


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

#37 2013-03-09 00:12:39

bobbym
Administrator

Online

Re: Simulations

There is only only more trick for the original problem.


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.

#38 2013-03-09 00:16:50

anonimnystefy
Real Member

Offline

Re: Simulations

Which is?


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

#39 2013-03-09 00:17:52

bobbym
Administrator

Online

Re: Simulations

It is not from 0 to 1. So you will have to do a change of variable to get it into that interval.


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.

#40 2013-03-09 00:21:37

anonimnystefy
Real Member

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Re: Simulations

What is not from 0 to 1?


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

#41 2013-03-09 00:23:16

bobbym
Administrator

Online

Re: Simulations

Look at the PDF in post #1. It  is from 1 to 2.


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.

#42 2013-03-09 00:25:30

anonimnystefy
Real Member

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Re: Simulations

Okay, so, what should I do?


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

#43 2013-03-09 00:28:13

bobbym
Administrator

Online

Re: Simulations

Make the substitution of x = x + 1. That produces a PDF from 0 to 1. Now do everything the same. You will get a histogram like the one in post #1. The expectation will be 1 less because of the substitution.


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.

#44 2013-03-09 00:32:05

anonimnystefy
Real Member

Offline

Re: Simulations

I am confused now.

Where and when do I make that substitution?


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

#45 2013-03-09 00:35:05

bobbym
Administrator

Online

Re: Simulations



Now just do everything the same.


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.

#46 2013-03-09 00:41:53

anonimnystefy
Real Member

Offline

Re: Simulations

I get

for the CDF.


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

#47 2013-03-09 00:48:47

bobbym
Administrator

Online

Re: Simulations

Hi;

Yes, that is correct. But we do not need it.


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.

#48 2013-03-09 00:50:11

anonimnystefy
Real Member

Offline

Re: Simulations

What do we need?

Oh, and I get


for the inverse.


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

#49 2013-03-09 00:53:06

bobbym
Administrator

Online

Re: Simulations

The integral from 0 to x, repeat post #33

The inverse is in terms of y.


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.

#50 2013-03-09 00:57:12

anonimnystefy
Real Member

Offline

Re: Simulations

Well, since the PDF is 0 for x<0, the integral from 0 to x is exactly the CDF.

Yes, it is. But what range should I have for y?


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

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