Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

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

The knowledge of some things as a function of age is a delta function.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,435

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.****If it ain't broke, fix it until it is.**

Offline

**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

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

The knowledge of some things as a function of age is a delta function.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,435

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

Offline

**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

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

The knowledge of some things as a function of age is a delta function.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,435

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.****If it ain't broke, fix it until it is.**

Offline

**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

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.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,435

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.****If it ain't broke, fix it until it is.**

Offline

**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

Post #104 told me sometying I had already known

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

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,435

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.****If it ain't broke, fix it until it is.**

Offline

**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

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

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,435

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.****If it ain't broke, fix it until it is.**

Offline

**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

Do you have another problem?

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,435

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.****If it ain't broke, fix it until it is.**

Offline

**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

Let's try math first.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,435

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.****If it ain't broke, fix it until it is.**

Offline

**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

Hi bobbym

14.7?

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,435

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.****If it ain't broke, fix it until it is.**

Offline

**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

Oh, but it does look like a CCP.

Any more?

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,435

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.****If it ain't broke, fix it until it is.**

Offline

**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

I solved it using absorbing Markov chains.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,435

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.****If it ain't broke, fix it until it is.**

Offline

**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

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)*

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,435

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.****If it ain't broke, fix it until it is.**

Offline

**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

Why 6/k?

Why should the anwser be a big surprise?

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

Offline