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#1 2012-11-04 10:54:50

anonimnystefy
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Posts: 15,417

Expectation

Here's a thread on expectation i.e. expected values. Post any problems on the mentioned subject here if yu want to. :-)

Last edited by anonimnystefy (2012-11-04 10:55:03)


“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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#2 2012-11-04 11:07:17

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 84,727

Re: Expectation

Hi;

problem 1
This one is easy ( sure it is, once you have seen it 151 times ).
What is the expected number of tosses of a coin before a head comes up. Show your answer in at least 4 different ways.


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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#3 2012-11-04 11:19:24

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,417

Re: Expectation

Hi bobbym


“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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#4 2012-11-04 11:28:58

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,727

Re: 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.

Online

#5 2012-11-04 11:36:15

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,417

Re: Expectation

Hi bobbym


“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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#6 2012-11-04 11:42:44

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,727

Re: Expectation

Hi;


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.

Online

#7 2012-11-04 11:46:24

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,417

Re: Expectation

Nope. It has a k in the exponent, not k-1. The probability of getting k heads before a tails appears is (1/2)^k and the probability that a tails then appears is 1/2.


“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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#8 2012-11-04 11:59:50

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 84,727

Re: Expectation

Could be a problem with the wording. In this case we count the toss where the head comes up too.


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.

Online

#9 2012-11-04 12:07:12

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,417

Re: Expectation

Yeah. I just assumed it to mean the number of tosses you do before (literally before) you toss a head comes up. Either way, that is one way of getting it. The other is to do a simulation, see what the result is empitically and then try to prove (or not dunno:) that the result is indeed what we got from the simulation. I haven't a clue about what two more metgods could be...


“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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#10 2012-11-04 12:17:25

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,727

Re: Expectation

Hi;


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.

Online

#11 2012-11-04 12:39:40

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,417

Re: Expectation

And the fourth?


“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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#12 2012-11-04 12:40:35

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,727

Re: Expectation

Markov chain is another way.


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.

Online

#13 2012-11-04 12:42:23

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,417

Re: Expectation

How would you do it with a Markov chain?


“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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#14 2012-11-04 12:52:45

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,727

Re: Expectation

Hi;


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.

Online

#15 2012-11-04 13:57:59

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,417

Re: Expectation

What do those entries represent?


“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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#16 2012-11-04 16:35:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,727

Re: Expectation

Hi;


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.

Online

#17 2012-11-04 18:36:56

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,417

Re: Expectation

No, because I don't know what you are refering to with Tmiss and Thit...


“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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#18 2012-11-04 18:48:12

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 84,727

Re: Expectation

Hi;

Not only is it badly labelled but see the two ones? That means two absorbing states, one for HH and one for TT. The chain ends when you get HH but not TT, so there should only be one absorbing state. Also it is too big.


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.

Online

#19 2012-11-05 01:45:49

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,417

Re: Expectation

Wouldn't (1/2 , 1/2 ; 0 , 1) be better?


“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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#20 2012-11-05 01:53:33

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,727

Re: Expectation

Hi;

That is correct! Know how to solve that?


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.

Online

#21 2012-11-05 02:02:20

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,417

Re: Expectation

Sum[P^n,n,0,infty] and take the term P[1,1]


“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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#22 2012-11-05 02:19:47

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,727

Re: Expectation

Hi;

That might be difficult to do. have you tried that?


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.

Online

#23 2012-11-05 02:32:22

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,417

Re: Expectation

It is very simple. The general nth power of that matrix is (1/2^n,1-(1/2^n) ; 0,1). It reduces to the sum we already have, so it gives confirmation of that sum.


“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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#24 2012-11-05 02:36:08

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,727

Re: Expectation

Hi;

The limit of that is

which is not correct.


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.

Online

#25 2012-11-05 02:42:21

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,417

Re: Expectation

It is correct. It just says that you are eventually bound to get a tails.


“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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