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#1 2013-03-26 20:46:31

Agnishom
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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'
'Who are you to judge everything?' -Alokananda

#2 2013-03-26 20:48:32

anonimnystefy
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Re: Another coin problem

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


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#3 2013-03-26 20:59:10

Agnishom
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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'
'Who are you to judge everything?' -Alokananda

#4 2013-03-26 21:33:41

bobbym
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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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#5 2013-03-26 21:35:57

Agnishom
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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'
'Who are you to judge everything?' -Alokananda

#6 2013-03-26 21:37:38

bobbym
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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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#7 2013-03-26 21:52:23

Agnishom
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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'
'Who are you to judge everything?' -Alokananda

#8 2013-03-26 21:54:47

Agnishom
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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 (2013-03-26 21:57:25)


'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'
'Who are you to judge everything?' -Alokananda

#9 2013-03-26 21:56:10

bobbym
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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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#10 2013-03-26 21:58:46

Agnishom
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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'
'Who are you to judge everything?' -Alokananda

#11 2013-03-26 22:07:41

bobbym
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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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#12 2013-03-26 22:09:19

Agnishom
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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'
'Who are you to judge everything?' -Alokananda

#13 2013-03-26 22:12:46

bobbym
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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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#14 2013-03-26 22:22:08

Agnishom
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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'
'Who are you to judge everything?' -Alokananda

#15 2013-03-26 22:23:25

bobbym
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Re: Another coin problem

You are a very clever person.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#16 2013-03-26 22:29:26

Agnishom
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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'
'Who are you to judge everything?' -Alokananda

#17 2013-03-26 22:30:02

bobbym
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Re: Another coin problem

Yes, I believe so.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#18 2013-03-26 22:50:22

Agnishom
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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'
'Who are you to judge everything?' -Alokananda

#19 2013-03-26 22:55:57

bobbym
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Re: Another coin problem

How did you do?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#20 2013-03-26 23:02:48

Agnishom
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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'
'Who are you to judge everything?' -Alokananda

#21 2013-03-26 23:03:42

bobbym
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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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#22 2013-03-26 23:14:28

Agnishom
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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'
'Who are you to judge everything?' -Alokananda

#23 2013-03-26 23:17:16

bobbym
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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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#24 2013-03-26 23:22:15

Agnishom
Real Member
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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'
'Who are you to judge everything?' -Alokananda

#25 2013-03-26 23:23:48

bobbym
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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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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