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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'

'Humanity is still kept intact. It remains within.' -Alokananda

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,532

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

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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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'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Hi;

You use the linearity of expectation.

**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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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'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

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

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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'

'Humanity is still kept intact. It remains within.' -Alokananda

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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'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

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

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Please see #8

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

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

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

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

Combinatorics is Algebra and Algebra is Combinatorics.

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What does that mean?

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

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

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)

.

.

.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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Yay got it

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

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

You are a very clever person.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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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'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

Yes, I believe so.

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

Combinatorics is Algebra and Algebra is Combinatorics.

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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'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

How did you do?

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

Combinatorics is Algebra and Algebra is Combinatorics.

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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'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

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

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

Combinatorics is Algebra and Algebra is Combinatorics.

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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'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

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

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

Combinatorics is Algebra and Algebra is Combinatorics.

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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'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,776

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

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

Combinatorics is Algebra and Algebra is Combinatorics.

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