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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi,

You're welcome.

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,882

Hi gAr;

Have you seen juans last 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.**

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Which one, finding miinimum value?

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,882

Hi;

Sorry, did not see he posted some after that. Take a look at this one. I solved it but in an unconvincing way.

**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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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Okay, I'll see that and post there if I have anything to say...

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,882

Thanks, that would be good. My answer is in post #33 of that thread.

**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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,882

**New Problem:**

**A and C are asked at their new job to tackle a problem. The casino would like to know what the expected difference is of the total of the first and the total of the second die if a pair are thrown 123456787654321 times. For example if a pair are thrown 3 times (3,6), (5,4), (1,1) the sum of the first die is 3+5+1=9 and the sum of the second die is 6+4+1=11 the difference is 2.**

**A instructs C to run a simulation assuring him that no mathematical solution is possible. He claims that his vast knowledge of meromorphic functions proves this. C believes him and runs a large simulation that takes 3 days of computer time.**

**The supervisor of the computing division is outraged at the 3 days usage and asks C for an explanation. C explains that he was correct and A agrees. The supervisor immediately fires A and C.**

**A and C immediately run back to B complaining about the supervisors treatment. B starts to laugh at their misfortune,**

**B says) You two turkeys really are overcooked. Of course there was a simple mathematical solution. You wasted 3 days on a giant mainframe and should be fired.**

**A says) Hold on B, I have had enough of your insolence. My mathematical knowledge dwarfs yours and that supervisor's too. I am right and we were fired unjustly.**

**D says) Here, here! A you are truly a champion of justice and mathematics too.**

**E says)A is a dullard and C is even worse for believing him!**

**Is A being fired cool with you? Is B right that they wasted the casino's money?**

**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: 15,606

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

bobbym wrote:

This prob came up somewhere else:

A coin with probability p of heads is tossed until a head appears for the first time. If the probability that the number of tosses required is {2,4,6,8,10...} is 2/5, then find p:

B solves it like this:

The chance that a head comes up on an even toss is:

Now sum that series:

Set the sum to 2/5 and solve for p.

Solve the equation any way you can, to get p = 1/3

Has B solved the problem?

Of course she has!

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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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

*Last edited by gAr (2012-07-11 19:13:52)*

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,882

Hi gAr;

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

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,882

Hi gAr;

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

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi,

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,882

Hi gAr;

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

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi,

I think we are not doing the same thing.

Suppose we throw the dice 4 times, (1,4), (5,3), (5,6), (2,3), we are taking absolute value of the difference? |(1+5+5+2)-(4+3+6+3)| = |13-16| = 3

Are we estimating the difference like that on the long run?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,882

Yes, that is what my example indicates. When I see a nice solution I get too excited and rush to post it. This has hurt me before and I must learn to slow down. To post it when I am sure I understand what was shown to me.

If we add the numbers like that the difference will approach zero. The expected value of both die will be 3.5.

I did not show the correct way to subtract the die!

(3,6) = 3

(5,1) = 4

(3,3) = 0

(5,6) = 1

(3+4+0+1) = 8

That is the correct way. Pairwise!

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

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,882

Hi;

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

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

*Last edited by gAr (2012-07-12 00:15:04)*

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,882

Hi;

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

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi,

But we are considering abasolute values, it must be increasing, isn't it?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,882

Hi;

I am pretty sure even with the absolute value the expected difference between 2 die can never be more than 5. (6,1) being the maximum. That is what this guys formula indicates. If I am wrong here it is because I did not present the problem correctly.

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

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Yeah, the way I understand the problem leads me nowhere else.

Perhaps you could post a code in procedural manner for simulation, so that I may understand the actual question?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 88,882

Hi gAr;

Okay, let's put into a form that we both agree on and gets the same answer he got. Do not worry I will send you the page when we are done so you can see what Robert Israel did without my interpretation getting in the way.

Here is the algorithm:

1)Pick two random integers in the interval [1,6].

2)Subtract them and take the absolute value.

3)Take the average of all of those values.

4) Print the answer.

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

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