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#151 2013-12-06 00:19:22

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: Probability problem.

Hi,


"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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#152 2013-12-06 00:22:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,771

Re: Probability problem.

Hi;

I had to trick it into getting an answer. Those are pretty tough integrals.

Where do those problems come from?


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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#153 2013-12-06 00:35:22

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: Probability problem.

Yes, they are tough. What trick did you perform?

You have been there before: http://people.missouristate.edu/lesreid/Adv97.html
(b) was a part I did thinking the answer would be same as (a)

Will be back soon.


"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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#154 2013-12-06 00:37:58

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,771

Re: Probability problem.

For one thing an assumption was necessary for theta and both integrals had to be done in pieces. For some reason this did the trick.

Forgot that place or lost the link.


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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#155 2013-12-06 00:58:43

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: Probability problem.

I see..
It's delightful to work on such problems.


"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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#156 2013-12-06 01:01:50

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,771

Re: Probability problem.

I agree. But they can be trying too.


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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#157 2013-12-06 01:09:48

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: Probability problem.

That's true, many things can go wrong here.
Simulation helps a ton!


"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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#158 2013-12-06 01:12:53

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,771

Re: Probability problem.

It sure does but sometimes even coming up with a simulation is difficult and time consuming.


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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#159 2013-12-06 01:21:11

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: Probability problem.

Yeah, sometimes, particularly when involving a geometrical shape instead of just points and lines.


"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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#160 2013-12-06 01:30:23

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,771

Re: Probability problem.

The circle is very tricky. I had to write new routines for generating points inside and on the circle that have the right distribution. It took a long time but next time I will be better prepared.


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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#161 2013-12-06 02:05:37

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: Probability problem.

Mark H. told me how to get the points.
r^2 must be uniformly distributed in [0,a^2]. Then take the root of the generated values.


"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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#162 2013-12-06 02:10:28

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,771

Re: Probability problem.

Hi;

What is that for?


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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#163 2013-12-06 02:13:54

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: Probability problem.

'a' is the given radius (In our problem, a=1). 'r' is the distance of P from center.


"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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#164 2013-12-06 02:19:51

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,771

Re: Probability problem.

So you used the square root of the random number you got from the uniform distribution twice to get (x,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.

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#165 2013-12-06 02:23:50

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: Probability problem.

Not twice, y can be fixed to 0.


"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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#166 2013-12-06 02:27:12

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,771

Re: Probability problem.

But if you wanted to fill the circle with that idea you would have to use it for both (x,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.

Offline

#167 2013-12-06 02:31:27

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: Probability problem.

To fill a circle, obtain random angles in [0, 2π), then the points would be (r cos θ, r sin θ).


"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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#168 2013-12-06 02:37:44

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,771

Re: Probability problem.

Hi;

That is close to what I did to. I will see you later, Thanks for the problems!


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

#169 2013-12-06 02:53:40

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: Probability problem.

Okay, see you later.


"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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#170 2013-12-06 04:04:56

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,849

Re: Probability problem.

Hi gAr

You're right. I misread the problem and thought the P is a point on the circle.


“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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#171 2013-12-06 04:12:30

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: Probability problem.

Hi anonimnystefy,

Okay.


"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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#172 2013-12-23 21:35:58

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: Probability problem.

New problem:

There are two fair, six sided dice.
'A' throws a die till she gets a sequence of '11'.
'B' throws the other die till he gets a sequence of '12'.
What is the probability that A throws the die more number of times than B?


"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

#173 2013-12-24 03:45:08

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,771

Re: Probability problem.

Hi gAr;


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

#174 2013-12-24 04:20:28

gAr
Member
Registered: 2011-01-09
Posts: 3,462

Re: Probability problem.

Hi bobbym,


"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

#175 2013-12-24 04:54:48

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,771

Re: Probability problem.

Hi gAr;


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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