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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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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?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,985

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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,985

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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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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.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,985

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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Post #104 told me sometying I had already known

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Well then, when I asked for another way you should have posted it prior to post #104

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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I did! It is in the first part of post #101!

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**bobbym****Administrator**- From: Bumpkinland
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Yes, I know but it is nice to see the formula actually in front of you...

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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Do you have another problem?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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I have many problems, social, psychological and math. Which do you want to try and solve?

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**anonimnystefy****Real Member**- From: The Foundation
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Let's try math first.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Okay.

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

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**anonimnystefy****Real Member**- From: The Foundation
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Hi bobbym

14.7?

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**bobbym****Administrator**- From: Bumpkinland
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Yes! Very good! Although it does not look like it that is a CCP.

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**anonimnystefy****Real Member**- From: The Foundation
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Oh, but it does look like a CCP.

Any more?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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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.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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I solved it using absorbing Markov chains.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Hmmm, mind If I see it? Then I can show you another way.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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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)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,985

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.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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Why 6/k?

Why should the anwser be a big surprise?

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