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You toss 25 coins.

What is the expected number of consecutive pair of heads?

Clarfication: for example, in a series of 6 coins if the result is HHTHHH then the number of consecutive pair of heads is 3

The answer is 6 according to an experiment......

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,821

The actual answer is 24*1/4=6 as well.

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

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Hmm .... How to do this?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,282

Hi;

You use the linearity of expectation.

**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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But I do not know about it!

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,282

Hi;

Okay, I will tell you what I know and please pay close attention to my signature.

Let Xi = 1 if the ith and (i+1)th coins are both heads, 0 otherwise, for i= 1,2,...,24.

E(Xi) = (1/2)(1/2) = 1/4.

Then the expected number of matches is

E(number of adj pairs) = 24 * (1/4) = 6.

Here we have used the theorem that E(X+Y) = E(X) +E(Y), which is true even if X and Y are not independent.

**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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What won't you tell those fools?

That explanation went away tangentially over my head.

What is this Xi?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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One minute, I went to the restroom and thought about it.

It seems I got the idea now

The probability that a coin and its next coin both are H is (1/4)

And as there are 24 coins (since there is no coin after the 25th), the Expected number of consecutive pair of heads is (1/4)*24

Have I got it correct?

Anyway whats xi?

*Last edited by Agnishom (2013-03-25 22:57:25)*

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,282

What won't you tell those fools?

Hey, that is pretty funny!

**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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Please see #8

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,282

That is the idea! You can multiply them because of the linearity of expectation.

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

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What does that mean?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,282

When you are multiplying by 24 you are actually adding 24 things up.

E(x+y) = E(x)+E(y)

E(x+y+z)=E(x)+E(y)+E(z)

.

.

.

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

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Yay got it

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,282

You are a very clever person.

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

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Are we still on the new s erver?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,282

Yes, I believe so.

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

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Hope you have already figured out, but in case you haven't : my exams just ended on March 22, 2013 1:35 PM IST

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,282

How did you do?

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

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Everything was okay except maths.

I am also afraid about Nky

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,282

What are you afraid of and why was math a problem?

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

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Math was a problem because:

1. We had to finish a 90 marks paper within 3 hours. Which is lengthy enough for maths.

2. I have a tendency to make silly mistakes which are further enhanced by point 1. as I didn't have time to revise the paper

3. I may have forgotten to do a trivial (or a nontrivial) in my paper.

4. I could not solve a problem, which carried four marks.

Moreover, everyone expects me to do extremely good in math

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,282

Sounds like a lot of pressure. You need a vacation.

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

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I have got a vacation.

The results of the exams are on 11th April and our new sessions start from the 12th

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,282

Oh, very good. I am being called away to do a chore. See you in a bit.

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

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