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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,676

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.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,658

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

How is the expected value 1/probability?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,676

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.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,658

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,676

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.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,658

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,676

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.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,658

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,676

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.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,658

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,676

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.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,658

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.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,676

Hi;

I am talking about the syntax of the commands.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,658

New problems?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,676

** 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.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,658

A standard French deck?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,676

Hi;

It is a regular deck of playing cards.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,658

Okay.

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,676

E(4 card deck) = 2 / 3

E(6 card deck) = 6 / 5

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,658

And E(8)?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,676

E(8 card deck) = 12 / 7

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,658

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,676

Hi;

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

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,658

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,676

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.**

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