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## #1 2013-04-14 20:41:55

evinda
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### Exercise in Probability!!!!

Hi!!!I hope you can help me at the following exercise:

We have a container that contains r balls that have numbers 1,...,r. We choose at random n of them without replacement. Let Y be the greatest and Z the smallest of the numbers of the balls we chose. Which are the probabilities P(Y<=y) and P(Z>=z)????

## #2 2013-04-14 21:51:53

bobbym

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### Re: Exercise in Probability!!!!

Hi;

Where does the problem come from? What textbook?

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.

## #3 2013-04-14 21:59:17

evinda
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### Re: Exercise in Probability!!!!

The problem comes from the book:Introduction to Probability Theory(P.HOEL,S.PORT,C.STONE)

## #4 2013-04-14 21:59:59

bobbym

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### Re: Exercise in Probability!!!!

Hi;

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.

## #5 2013-04-14 22:12:53

evinda
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### Re: Exercise in Probability!!!!

It is in the capital 3,the exercise 12....

## #6 2013-04-14 22:47:50

bobbym

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### Re: Exercise in Probability!!!!

Hi;

Okay, thank you. I will work on it? Do you have anything that can help?

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.

## #7 2013-04-14 22:55:45

evinda
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### Re: Exercise in Probability!!!!

I think I have to use {n choose r},but I am not sure

## #8 2013-04-14 23:14:19

anonimnystefy
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### Re: Exercise in Probability!!!!

I am getting

Last edited by anonimnystefy (2013-04-14 23:52:06)

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

## #9 2013-04-14 23:18:13

evinda
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### Re: Exercise in Probability!!!!

And how can I prove this???

## #10 2013-04-14 23:19:15

anonimnystefy
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### Re: Exercise in Probability!!!!

Well, I used the inclusion-exclusion principle on the negative event.

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

## #11 2013-04-14 23:19:30

bobbym

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### Re: Exercise in Probability!!!!

Ooooh that is nice one. I have a better question... Where did you get it 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.

## #12 2013-04-14 23:26:56

anonimnystefy
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### Re: Exercise in Probability!!!!

Get what from?

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

## #13 2013-04-14 23:30:20

bobbym

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### Re: Exercise in Probability!!!!

Ooooh that is a good one! You are in good form today. What? I certainly did not mean the Eiffel tower. The equation, I do not know it. So I figure it is some book that I skipped over.

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.

## #14 2013-04-14 23:32:24

anonimnystefy
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### Re: Exercise in Probability!!!!

It can be found in any common textbook. |AuB|=|A|+|B|-|AnB|.

Last edited by anonimnystefy (2013-04-14 23:36:35)

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

## #15 2013-04-14 23:37:05

bobbym

Online

### Re: Exercise in Probability!!!!

Which common one would you recommend?

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.

## #16 2013-04-14 23:38:41

anonimnystefy
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### Re: Exercise in Probability!!!!

Well, I do not know of any you could read, but there is an article on Wikipedia on it. Search for "inclusion exclusion principle".

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

## #17 2013-04-14 23:45:10

bobbym

Online

### Re: Exercise in Probability!!!!

The Wikipedia article covers PIE but it does not explain the formula in post #8.

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.

## #18 2013-04-14 23:47:09

anonimnystefy
Real Member

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### Re: Exercise in Probability!!!!

No, I derived the formula myself using the PIE.

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

## #19 2013-04-14 23:48:22

bobbym

Online

### Re: Exercise in Probability!!!!

Hmmm, have you tested this formula?

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.

## #20 2013-04-14 23:50:37

anonimnystefy
Real Member

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### Re: Exercise in Probability!!!!

Hm, I just found an error concerning the numbers. Let me fix the formula.

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

## #21 2013-04-15 00:08:13

bobbym

Online

### Re: Exercise in Probability!!!!

Did you fix it? Now how about a verification?

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.

## #22 2013-04-15 00:09:39

anonimnystefy
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### Re: Exercise in Probability!!!!

Which kind of verification do you need?

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

## #23 2013-04-15 00:12:57

bobbym

Online

### Re: Exercise in Probability!!!!

We could run a simulation. We could substitute numbers and at least see whether the formula works for a few examples. It can not prove the correctness of it but it sure can prove it false.

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.

## #24 2013-04-15 00:19:25

anonimnystefy
Real Member

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### Re: Exercise in Probability!!!!

I tested for a few values and it works.

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

bobbym

Online