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.

#2026 2014-01-31 22:07:52

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,574

Re: Is this cool with you?

Hi;

Okay, take your time, I will wait.


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.

Offline

#2027 2014-01-31 23:32:22

gAr
Member
Registered: 2011-01-09
Posts: 3,478

Re: Is this cool with you?

Hi bobbym,

I think these must be right, finally!

1)


where 'n_a' is any of the number of cards available of digit 'a' and 'h' is the number of cards greater than 'a'.

2)

3)

4)

For (9,9,7),

And the expected sum of the highest three, using the above equations:


"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."

Offline

#2028 2014-02-01 01:27:57

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,574

Re: Is this cool with you?

Hi;

H = 24, how would you phrase that? Cards less then a?


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.

Offline

#2029 2014-02-01 01:35:49

gAr
Member
Registered: 2011-01-09
Posts: 3,478

Re: Is this cool with you?

Hi,

'h' is the number of cards having face value > 'a'

For the example, a=7 and 'h' includes all 8's, 9's and 10's: h=4+4+16


"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."

Offline

#2030 2014-02-01 01:45:48

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,574

Re: Is this cool with you?

Very good! I am checking the last one now and you have an important result!

Could you please explain what f\goes into what for your formula 4).

The example is (7,7,9)


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.

Offline

#2031 2014-02-01 01:59:22

gAr
Member
Registered: 2011-01-09
Posts: 3,478

Re: Is this cool with you?

Yeah, but took quite a while to correct a mistake in my program!

For (7,7,9),
a=7, b=9, h=24, n7=n9=4


"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."

Offline

#2032 2014-02-01 02:00:21

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,574

Re: Is this cool with you?

Hi;

I will run it through your fourth formula.


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.

Offline

#2033 2014-02-01 02:12:07

gAr
Member
Registered: 2011-01-09
Posts: 3,478

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."

Offline

#2034 2014-02-01 02:12:56

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,574

Re: Is this cool with you?

Hi;

Did you see the top part of post #2030?


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.

Offline

#2035 2014-02-01 02:27:03

gAr
Member
Registered: 2011-01-09
Posts: 3,478

Re: Is this cool with you?

Hi,

Yes, the top part of my reply was refering to my program for calculating the expectation.
I saw that was what you actually wanted!

Also saw that it was already asked in "help me", good question!

Would you like me to post my code in "computer math" ?


"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."

Offline

#2036 2014-02-01 02:29:51

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,574

Re: Is this cool with you?

I saw that was what you actually wanted!

You read the future.

http://www.mathisfunforum.com/viewtopic.php?id=13145


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.

Offline

#2037 2014-02-01 02:41:42

gAr
Member
Registered: 2011-01-09
Posts: 3,478

Re: Is this cool with you?

You read the future.

Nope, math.se!


Yes, I was talking about that thread.


"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."

Offline

#2038 2014-02-01 02:45:07

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,574

Re: Is this cool with you?

That was me. Why the heck did you not post in there?


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.

Offline

#2039 2014-02-01 02:58:28

gAr
Member
Registered: 2011-01-09
Posts: 3,478

Re: Is this cool with you?

I have forgotten my login credentials there, had registered once a long time ago.
Never mind, you post the answers there you now know.

We can easily extend the formula for any number of picks. But more cases if we need sum of 'n' highest cards, with n>3. I wonder if the cases can be eliminated altogether!


"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."

Offline

#2040 2014-02-01 03:01:08

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,574

Re: Is this cool with you?

They do not get those answers. They belong to you and it is your choice whether or not to share them.

I have been working on using order statistics for the problem but have not been successful.


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.

Offline

#2041 2014-02-01 03:10:04

gAr
Member
Registered: 2011-01-09
Posts: 3,478

Re: Is this cool with you?

I don't mind you sharing the answer there.


The 10's have a different probability, that's the difficulty we have here.
Otherwise, we might have had a better answer.


"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."

Offline

#2042 2014-02-01 03:18:35

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,574

Re: Is this cool with you?

I am hazy on this whole idea so it might be wrong but there is a distribution called the Empirical Distribution which handles 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.

Offline

#2043 2014-02-01 03:21:50

gAr
Member
Registered: 2011-01-09
Posts: 3,478

Re: Is this cool with you?

Okay, I'll check that.
Taking a break now, see you later.


"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."

Offline

#2044 2014-02-01 03:24:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,574

Re: Is this cool with you?

Okay, and thanks for coming in.


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.

Offline

#2045 2014-02-03 18:18:27

gAr
Member
Registered: 2011-01-09
Posts: 3,478

Re: Is this cool with you?

Here's a formula for probability of the order statistic:

E.g. For the probability that 6th highest number is 7 among 8 selected, we have:

I don't know a formula for joint distribution yet.

The literature on these look stupid without any example.


"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."

Offline

#2046 2014-02-03 20:55:40

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,574

Re: Is this cool with you?

Hi gAr;

I have had much trouble with the order statistic of an empirical distribution like these. What literature are you looking at?


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.

Offline

#2047 2014-02-03 21:09:04

gAr
Member
Registered: 2011-01-09
Posts: 3,478

Re: Is this cool with you?

Hi,

I had not tried order statistics of discrete distributions before, the formulas in the program had Vandermonde's identity in it.

Literature, whatever I could find online.
I tried the formula in wikipedia, but couldn't understand what to make of f(x) and F(x).

I also looked at "A first course on order statistics", doesn't have a single numerical example!


"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."

Offline

#2048 2014-02-03 21:13:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,574

Re: Is this cool with you?

I think I remember that book, I had to throw it away for that very reason.


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.

Offline

#2049 2014-02-03 21:16:54

gAr
Member
Registered: 2011-01-09
Posts: 3,478

Re: Is this cool with you?

If we can get a formula for joint distribution, our job for the expected sum will be done!


"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."

Offline

#2050 2014-02-03 21:28:03

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,574

Re: Is this cool with you?

That has been difficult for me. Mathematica has a command to do all these type problems but when I try to have the command work on an empirical distribution like this one it fails. This has been the major problem, I can not get exact answers and must rely on simulations which are not close enough.


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.

Offline

Board footer

Powered by FluxBB