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#2051 2014-02-03 21:32:40

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

Re: Is this cool with you?

I see.
For now, simulations for me too.


"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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#2052 2014-02-03 21:36:52

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

Re: Is this cool with you?

Your formula does look interesting though and I will play with it. Who knows, I might get lucky.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#2053 2014-02-03 21:48:01

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

Re: Is this cool with you?

Yes, I'm also working on it.


"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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#2054 2014-02-04 23:01:27

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

Re: Is this cool with you?

Here's a joint distribution formula for four consecutive terms:

l_a : no. of cards less than a
s_b : number of cards selected having face value of b
nh : no. of positions available after placing the given 4 numbers

E.g.

Suppose we wanted to know the probability of sorted order to be 5 6 7 8, starting from 4th position:
We take the variables as:

5 5 5 8:

5 5 5 5: change s_d to s_a in the formula and

Last edited by gAr (2014-02-04 23:03:45)


"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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#2055 2014-02-05 05:49:23

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

Re: Is this cool with you?

Hi gAr;

I was busy doing some chores so I could not get to it till now. I will try it on some problems.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#2056 2014-02-05 06:18:10

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

Re: Is this cool with you?

Hi,

Okay.


"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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#2057 2014-02-05 06:20:56

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

Re: Is this cool with you?

Found the Kendall books but have not looked through them yet.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#2058 2014-02-05 15:37:44

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

Re: Is this cool with you?

Hi,

Which book is that?


"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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#2059 2014-02-05 16:08:36

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

Re: Is this cool with you?

The ones on Advanced Statistics. So far they are not very good.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#2060 2014-02-05 21:00:45

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

Re: Is this cool with you?

Okay.


"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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#2061 2014-02-06 01:42:04

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

Re: Is this cool with you?

They claimed that the books were used for the writing of the probability routines in Maple. I got little out of them so far.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#2062 2014-02-06 01:44:06

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

Re: Is this cool with you?

I see.


"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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#2063 2014-02-06 02:50:27

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

Re: Is this cool with you?

Hi gAr;

Suppose we wanted to know the probability of sorted order to be 5 6 7 8, starting from 4th position:

Does this mean x x x x 5 6 7 8, where x are cards?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#2064 2014-02-06 04:34:48

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

Re: Is this cool with you?

Hi,

...  starting from 4th position

x x x 5 6 7 8 x


"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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#2065 2014-02-06 04:38:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

Re: Is this cool with you?

Oh boy, I forgot how to count!


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#2066 2014-02-06 05:18:41

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

Re: Is this cool with you?

Never mind, happens!


"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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#2067 2014-02-06 05:41:33

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

Re: Is this cool with you?

Hi gAr;

For your first example of 5,6,7,8 ( x x x 5 6 7 8 x ) I am getting a simulation answer about 1 / 10 th as large as predicted. What are you getting?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#2068 2014-02-06 15:50:08

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

Re: Is this cool with you?

Hi,

My simulation answer is close: 0.0056
From the formula: 4162400 / C(52,8)


"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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#2069 2014-02-06 20:08:34

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

Re: Is this cool with you?

That is very close to what I am getting with a simulation too. But the formula is not giving that answer. I will check that I have not made some error.

Okay, first problem checks out. On to the second one.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#2070 2014-02-06 22:54:17

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

Re: Is this cool with you?

You got it right?


"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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#2071 2014-02-07 01:27:22

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

Re: Is this cool with you?

Hi gAr;

I finally got the same answer you did. Then I had connection problems for 5 hours finally got back online.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#2072 2014-02-07 02:23:53

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

Re: Is this cool with you?

Hi,

That's good!


"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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#2073 2014-02-07 13:35:10

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

Re: Is this cool with you?

Hi gAr;

The second example checks out and on to the third...

Update:

The third example checks out! Ooooba oooba oooba, oooga ooog ooga! That means Wunderbar!


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#2074 2014-03-19 13:40:23

eigenguy
Member
Registered: 2014-03-18
Posts: 78

Re: Is this cool with you?

Forgive me, please, for taking this thread all the way back to the beginning, and also if someone else has pointed this out in those thousands of posts I have despaired of hunting through to check:

bobbym wrote:

How would you judge this answer? And why?

The question itself and the replies given suggest this is wrong, but I would judge this answer correct. The following theorems are all easily proved:

The calculation shown follows from them.


"Having thus refreshed ourselves in the oasis of a proof, we now turn again into the desert of definitions." - Bröcker & Jänich

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#2075 2014-03-19 14:23:22

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,249

Re: Is this cool with you?

Hi;

Did you see post #9 in this same thread?

Scientia and JFF are well grounded in questions like these.

Their complaint starts right here:

Courtesy of Wikipedia:

If f is a real-valued (or complex-valued) function, then taking the limit is compatible with the algebraic operations, provided the limits on the right sides of the equations below exist (the last identity only holds if the denominator is non-zero). This fact is often called the algebraic limit theorem.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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