Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#126 2012-11-09 05:52:25

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,999

Re: Expectation

The expected value is 1/probability is it not?

The matrix when computed should be 13.7


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

#127 2012-11-09 06:07:04

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Expectation

http://www.wolframalpha.com/input/?t=cr … 5%2F6))%5D

How is the expected value 1/probability?


“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

Offline

#128 2012-11-09 06:17:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,999

Re: Expectation

Hi;

You did not enter the problem correctly
Matrix Inverse( IdentityMatrix[6] -  {{0,1,0,0,0,0 }, {0,1/6,5/6,0,0,0} ,{ 0,0,1/3,2/3,0,0} ,{ 0,0,0,1/2,1/2,0} ,{ 0,0,0,0,2/3,1/3} , {0,0,0,0,0,5/6 }}).{{1},{1},{1},{1},{1},{1}} gives the right result.

If the probability is 1 / 6 of something happening then we expect it to happen once in 6 times.


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

#129 2012-11-09 06:27:35

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Expectation

My result is correct. I just didn't sum the first row.


“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

Offline

#130 2012-11-09 06:42:45

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,999

Re: Expectation

When I entered yours it says the trace is 14.7. The trace is the sum of the diagonal elements. It may or may not be correct.


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

#131 2012-11-09 06:47:32

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Expectation

The trace and the sum of the first row are the same for that matrix.


“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

Offline

#132 2012-11-09 07:09:10

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,999

Re: Expectation

Yes, but are you sure that will always be the case?

This way spits the answer out in a form that is easy to understand.


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

#133 2012-11-09 08:19:59

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Expectation

No, I sum the first row. WA is the one who thinks you need the trace.


“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

Offline

#134 2012-11-09 08:30:46

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,999

Re: Expectation

Hi;

When I run your link, I get this result. That is clearly not the right answer.

For one thing he did not interpret the identitymatrisx command correctly. For another the inverse was not calculated...

I would do it the way I showed in post#128.

Taking a little break.

View Image: 2012-11-09_122903.gif

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

#135 2012-11-09 08:45:29

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Expectation

That is not the same result I am getting when I press the link.


“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

Offline

#136 2012-11-09 09:19:46

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,999

Re: Expectation

Supposing others get my result? Isn't my way more reliable, since we are both getting the same answer. Also, my syntax is much closer to the package's syntax.


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

#137 2012-11-09 09:59:40

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Expectation

You just had multiplication by the vector (1,1,1,1,1,1) and I did the multiplication by hand. It is the same method.


“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

Offline

#138 2012-11-09 10:23:12

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,999

Re: Expectation

Hi;

I am talking about the syntax of the commands.


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

#139 2012-11-10 11:07:21

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Expectation

New problems?


“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

Offline

#140 2012-11-10 11:51:12

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,999

Re: Expectation

A deck of cards are dealt out in a circle. What is the expected number of pairs of adjacent cards which are both black?


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

#141 2012-11-10 11:57:08

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Expectation

A standard French deck?


“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

Offline

#142 2012-11-10 12:31:46

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,999

Re: Expectation

Hi;

It is a regular deck of playing cards.


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

#143 2012-11-10 12:39:58

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Expectation

Okay.

What do you get as the answer for decks of 4 and 6 cards (half of which are black)?


“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

Offline

#144 2012-11-10 12:46:15

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,999

Re: Expectation

E(4 card deck) = 2 / 3

E(6 card deck) = 6 / 5


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

#145 2012-11-10 12:58:07

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Expectation

And E(8)?


“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

Offline

#146 2012-11-10 13:08:29

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,999

Re: Expectation

E(8 card deck) = 12 / 7


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

#147 2012-11-18 12:29:44

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Expectation

I haven't been able to find a solution...


“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

Offline

#148 2012-11-18 12:31:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,999

Re: Expectation

Hi;

Okay, I can give the answer if you want it.


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

#149 2012-11-18 12:33:15

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,606

Re: Expectation

I'd rather get a method than an answer, but either is okay...


“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

Offline

#150 2012-11-18 12:43:51

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,999

Re: Expectation

Hi;

I'd rather get a method than an answer,

Hmmmm. You should already have the answer or darn close to one. Have you forgotten how we work?


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

Board footer

Powered by FluxBB