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#1 2013-04-13 22:41:55

evinda
Member
Registered: 2013-04-13
Posts: 105

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)????

Thanks in advance!!!!!

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#2 2013-04-13 23:51:53

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,705

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#3 2013-04-13 23:59:17

evinda
Member
Registered: 2013-04-13
Posts: 105

Re: Exercise in Probability!!!!

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

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#4 2013-04-13 23:59:59

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,705

Re: Exercise in Probability!!!!

Hi;

Page and number please?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#5 2013-04-14 00:12:53

evinda
Member
Registered: 2013-04-13
Posts: 105

Re: Exercise in Probability!!!!

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

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#6 2013-04-14 00:47:50

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,705

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#7 2013-04-14 00:55:45

evinda
Member
Registered: 2013-04-13
Posts: 105

Re: Exercise in Probability!!!!

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

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#8 2013-04-14 01:14:19

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,525

Re: Exercise in Probability!!!!

I am getting

Last edited by anonimnystefy (2013-04-14 01:52:06)


“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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#9 2013-04-14 01:18:13

evinda
Member
Registered: 2013-04-13
Posts: 105

Re: Exercise in Probability!!!!

And how can I prove this??? hmm

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#10 2013-04-14 01:19:15

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,525

Re: Exercise in Probability!!!!

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


“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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#11 2013-04-14 01:19:30

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,705

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#12 2013-04-14 01:26:56

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,525

Re: Exercise in Probability!!!!

Get what from?


“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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#13 2013-04-14 01:30:20

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,705

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#14 2013-04-14 01:32:24

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,525

Re: Exercise in Probability!!!!

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

Last edited by anonimnystefy (2013-04-14 01:36:35)


“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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#15 2013-04-14 01:37:05

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,705

Re: Exercise in Probability!!!!

Which common one would you recommend?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#16 2013-04-14 01:38:41

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,525

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".


“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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#17 2013-04-14 01:45:10

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,705

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#18 2013-04-14 01:47:09

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,525

Re: Exercise in Probability!!!!

No, I derived the formula myself using the PIE.


“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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#19 2013-04-14 01:48:22

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,705

Re: Exercise in Probability!!!!

Hmmm, have you tested this formula?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#20 2013-04-14 01:50:37

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,525

Re: Exercise in Probability!!!!

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


“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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#21 2013-04-14 02:08:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,705

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#22 2013-04-14 02:09:39

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,525

Re: Exercise in Probability!!!!

Which kind of verification do you need?


“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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#23 2013-04-14 02:12:57

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,705

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#24 2013-04-14 02:19:25

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,525

Re: Exercise in Probability!!!!

I tested for a few values and it works.


“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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#25 2013-04-14 02:24:10

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,705

Re: Exercise in Probability!!!!

M code please?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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