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#101 2012-11-08 09:52:43

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Expectation

From the definition of expectation..

bobbym wrote:

Hi;

That is not right either. Actually, the problem is related to a CCP but we have not covered that yet.

What is CCP?


“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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#102 2012-11-08 09:54:55

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 88,998

Re: Expectation

We have not come to it yet but we soon will. Do you know another way for the last problem?


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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#103 2012-11-08 09:57:06

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Expectation

I do not.


“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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#104 2012-11-08 09:59:49

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 88,998

Re: Expectation

Hi;


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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#105 2012-11-08 10:01:49

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Expectation

anonimnystefy wrote:

From the definition of expectation..

bobbym wrote:

Hi;

That is not right either. Actually, the problem is related to a CCP but we have not covered that yet.

What is CCP?

Did you not see the first sentence of this post?


“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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#106 2012-11-08 10:02:55

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,998

Re: Expectation

Yes, I did and I said we have not got to it yet. CCP is short for Coupon Collector Problem.


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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#107 2012-11-08 10:08:34

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Expectation

No, I didn't mean that. The text before the quote is on its own. It is not conected to the rest of the post. It was an answer to your previously asked question.


“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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#108 2012-11-08 10:09:52

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,998

Re: Expectation

I see, but I think I already answered the question with post #104.


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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#109 2012-11-08 10:11:41

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Expectation

Post #104 told me sometying I had already known

Last edited by anonimnystefy (2012-11-08 10:12:10)


“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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#110 2012-11-08 10:12:45

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 88,998

Re: Expectation

Well then, when I asked for another way you should have posted it prior to post #104


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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#111 2012-11-08 10:17:11

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Expectation

I did! It is in the first part of post #101!


“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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#112 2012-11-08 10:19:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,998

Re: Expectation

Yes, I know but it is nice to see the formula actually in front of you...


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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#113 2012-11-08 10:29:49

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Expectation

Do you have another 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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#114 2012-11-08 10:30:58

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,998

Re: Expectation

I have many problems, social, psychological and math. Which do you want to try and solve?


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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#115 2012-11-08 10:32:50

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Expectation

Let's try math first.


“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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#116 2012-11-08 10:35:27

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,998

Re: Expectation

Okay.

What is the expected number of times a fair die must be rolled until all scores appear at least once?


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

#117 2012-11-08 11:39:29

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Expectation

Hi bobbym

14.7?


“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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#118 2012-11-08 11:43:39

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,998

Re: Expectation

Yes! Very good! Although it does not look like it that is a CCP.


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

#119 2012-11-08 11:58:08

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Expectation

Oh, but it does look like a CCP.

Any more?


“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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#120 2012-11-08 12:04:51

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,998

Re: Expectation

First, how did you solve the last one?

Just one or two more of these lightweight problems and we can move on to tougher ones.


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

#121 2012-11-08 20:22:12

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Expectation

I solved it using absorbing Markov chains.


“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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#122 2012-11-08 21:02:33

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,998

Re: Expectation

Hmmm, mind If I see it? Then I can show you 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

#123 2012-11-09 02:24:43

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Expectation

It's a pretty large one to do by hand.

(0,1,0,0,0,0,0)
(0,1/6,5/6,0,0,0,0)
(0,0,1/3,2/3,0,0,0)
(0,0,0,1/2,1/2,0,0)
(0,0,0,0,2/3,1/3,0)
(0,0,0,0,0,5/6,1/6)
(0,0,0,0,0,0,1)

Last edited by anonimnystefy (2012-11-09 02:25:14)


“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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#124 2012-11-09 02:48:51

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,998

Re: Expectation

Hi;

You did forget the labels but here is another way.

The expected wait for all scores to appear = expected wait for one score +
expected wait for second score + ... + expected wait for sixth and final score.
The probabilities of these events are, respectively, 6/6, 5/6, 4/6, 3/6, 2/6, 1/6.
Therefore the expected wait for all scores to appear?

It's a pretty large one to do by hand.

No one but a lunatic would want to.

When you computed the answer you should have got a big surprise.


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

#125 2012-11-09 05:45:09

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Expectation

Why 6/k?

Why should the anwser be a big surprise?


“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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