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#1 2013-03-25 21:46:31

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
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Another coin problem

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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#2 2013-03-25 21:48:32

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: Another coin problem

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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#3 2013-03-25 21:59:10

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
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Re: Another coin problem

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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#4 2013-03-25 22:33:41

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,870

Re: Another coin problem

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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#5 2013-03-25 22:35:57

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

Re: Another coin problem

But I do not know about it! sad


'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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#6 2013-03-25 22:37:38

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,870

Re: Another coin problem

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.

Online

#7 2013-03-25 22:52:23

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

Re: Another coin problem

What won't you tell those fools?

That explanation went away tangentially over my head.
What is this Xi?


'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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#8 2013-03-25 22:54:47

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

Re: Another coin problem

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)


'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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#9 2013-03-25 22:56:10

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,870

Re: Another coin problem

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.

Online

#10 2013-03-25 22:58:46

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

Re: Another coin problem

Please see #8


'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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#11 2013-03-25 23:07:41

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,870

Re: Another coin problem

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.

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.

Online

#12 2013-03-25 23:09:19

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

Re: Another coin problem

What does that mean?


'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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#13 2013-03-25 23:12:46

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,870

Re: Another coin problem

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.

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.

Online

#14 2013-03-25 23:22:08

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

Re: Another coin problem

Yay got 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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#15 2013-03-25 23:23:25

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,870

Re: Another coin problem

You are a very clever person.


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.

Online

#16 2013-03-25 23:29:26

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

Re: Another coin problem

Are we still on the new s erver?


'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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#17 2013-03-25 23:30:02

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,870

Re: Another coin problem

Yes, I believe so.


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.

Online

#18 2013-03-25 23:50:22

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

Re: Another coin problem

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


'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

Offline

#19 2013-03-25 23:55:57

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,870

Re: Another coin problem

How did you do?


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.

Online

#20 2013-03-26 00:02:48

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

Re: Another coin problem

Everything was okay except maths. sad

I am also afraid about Nky


'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

Offline

#21 2013-03-26 00:03:42

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,870

Re: Another coin problem

What are you afraid of and why was math a 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.

Online

#22 2013-03-26 00:14:28

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

Re: Another coin problem

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


'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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#23 2013-03-26 00:17:16

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,870

Re: Another coin problem

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


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.

Online

#24 2013-03-26 00:22:15

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

Re: Another coin problem

I have got a vacation.
The results of the exams are on 11th April and our new sessions start from the 12th


'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

Offline

#25 2013-03-26 00:23:48

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,870

Re: Another coin problem

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.

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.

Online

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