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#51 2012-11-06 10:18:43

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,866

Re: Expectation

What!!!!! Then you can never understand why I vote!


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#52 2012-11-06 10:21:15

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Expectation

Okay.

Got a new problem?


“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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#53 2012-11-06 10:23:47

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,866

Re: Expectation

My, we are in a talkative mood today.

What is the expected number of throws of a single die before a (1,1) comes up?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#54 2012-11-06 10:27:37

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Expectation

42?


“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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#55 2012-11-06 10:31:47

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,866

Re: Expectation

Hi;

Two ways to justify that?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#56 2012-11-06 10:34:19

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Expectation

Yup! A formula just like yours for the last problem and a Markov chain.


“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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#57 2012-11-06 10:37:16

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,866

Re: Expectation

I am putting my turban on my head. I am saying the magic words. Sorry, it is not working, I can not see your solution.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#58 2012-11-06 10:45:33

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Expectation

Don't you believe me?

Markov chain:
((5/6,1/6,0);(5/6,0,1/6);(0,0,1))

A formula:
E=5/6 * (E+1) + 1/6 * 5/6 * (E+2) + 1/6 * 1/6 * 2


“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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#59 2012-11-06 10:49:43

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,866

Re: Expectation

Very good! The young learn quickly.

Want more?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#60 2012-11-06 10:59:24

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Expectation

Of course! I have a feeling the next problem will be devilish...


“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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#61 2012-11-06 11:03:12

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,866

Re: Expectation

Oh yes! Hellish.

Cards from a well shuffled deck are dealt to you one at a time. What is the expected number of cards till you hold 10 hearts?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#62 2012-11-06 11:08:15

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Expectation

It seems like it is just meant to confuse me, because I am getting 52 (assuming the standard number of cards in the deck)...


“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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#63 2012-11-06 11:09:31

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,866

Re: Expectation

Yes, it is designed to confuse you and it has. Can you not get 10 hearts in under 52 cards?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#64 2012-11-06 11:15:34

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Expectation

You almost got me fooled there. I think the answer is 53/2.


“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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#65 2012-11-06 11:19:21

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,866

Re: Expectation

Hi;

That is not correct.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#66 2012-11-06 11:21:28

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Expectation

Oh, wait! I tought it said 10 of hearts. Let me try again.


“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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#67 2012-11-06 11:34:56

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Expectation

New answer: 265/7?


“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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#68 2012-11-06 11:38:52

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,866

Re: Expectation

Hmmmm... Your method was?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#69 2012-11-06 11:43:57

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Expectation

Found it from the definition of expectation:

Sum[i*Binomial[13,10]*10*Binomial[39,i-10]*(i-1)!*(52-i)!/52!,i,10,52]


“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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#70 2012-11-06 11:46:41

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,866

Re: Expectation

Hi;

That is very good, I did not know that one. And another way is?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#71 2012-11-06 11:48:54

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Expectation

I have no idea.


“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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#72 2012-11-06 11:52:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,866

Re: Expectation

The negative hypergeometric distribution is another way.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#73 2012-11-06 12:04:52

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Expectation

I have not even a slightest idea what that is.


“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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#74 2012-11-06 12:07:05

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,866

Re: Expectation

The discrete distributions borrowed from statistics are of great help.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#75 2012-11-07 01:39:14

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Expectation

I still have no idea what that is.

Do you have a new problem?


“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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