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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

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: 86,228

Hi;

**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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

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: 86,228

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

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.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

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
- Posts: 86,228

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

Do you have another problem?

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

Let's try math first.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

Okay.

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

Hi bobbym

14.7?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

Oh, but it does look like a CCP.

Any more?

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

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.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

I solved it using absorbing Markov chains.

Here lies the reader who will never open this book. He is forever dead.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

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

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

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.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,228

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.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

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.

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