Mean position value for each in the 6/49 game ?
Stig Holmquist
game and what would be the std.dev. for each?
Stig Holmquist
Stig Holmquist
A simulation wwith 10 million done by a friend yielded numbers very
close to units of 50/7, which I guess would be the theoretical.
Stig
me13013
> On Sat, 07 Nov 2009 13:42:10 -0500, Stig Holmquist
>
> >How close to units of 7 would the mean position value be for the 6/49
> >game and what would be the std.dev. for each?
>
> >Stig Holmquist
>
> A simulation wwith 10 million done by a friend yielded numbers very
> close to units of 50/7, which I guess would be the theoretical.
>
> Stig
It might be helpful if you described what the 6/49 game is and what
you mean by "mean position value". I for one have no idea what you're
talking about, except that it must have something to do with
lotteries.
Bob H
James Dow Allen
> >How close to units of 7 would the mean position value be for the 6/49
> >game and what would be the std.dev. for each?
What you're asking I think, is:
What is the mean and standard deviation
for each X_i
where (X_1, X_2, ..., X_6)
is taken over all *sorted* combinations of
(1,2,3,...,49}
> A simulation wwith 10 million done by a friend yielded numbers very
> close to units of 50/7, which I guess would be the theoretical.
Why "simulate" 10 million trials, when with
14 million "trials" one can generate *all* combinations?
Here's what I got:
X_1 7.142857 sd=5.736564
X_2 14.285714 sd=7.405872
X_3 21.428571 sd=8.112726
X_4 28.571429 sd=8.112726
X_5 35.714286 sd=7.405872
X_6 42.857143 sd=5.736564
Means are as expected. Don't know how easy
it would be to get sd's without brute force.
In lieu of a .sig, I've appended a C program
to print all 13,983,816 possible Lotto tickets!
Combination generation is done by Payne's
algorithm (Knuth 7.2.1.3 - Algo R).
James Dow Allen
int main(void)
{
int revarr[7], i, j, a0, a1;
for (j = 0; j < 6; j++)
revarr[j] = j;
revarr[j] = 49;
do {
for (i = 0; i < 6; i++)
printf(" %d", revarr[i] + 1);
printf("\n");
a0 = revarr[0];
a1 = revarr[1];
if (a0 > 0) {
revarr[0] = a0 - 1;
continue;
} else if (a1 + 1 < revarr[2]) {
revarr[0] = a1;
revarr[1] = a1 + 1;
continue;
} else {
j = 2;
a0 = a1;
a1 = revarr[2];
}
while (j < 6) {
if (a1 > j) {
revarr[j] = a0;
revarr[j-1] = j - 1;
break;
}
a0 = a1;
a1 = revarr[++j];
if (a1 + 1 < revarr[j + 1]) {
revarr[j-1] = a1;
revarr[j] = a1 + 1;
break;
}
a0 = a1;
a1 = revarr[++j];
}
} while (j < 6);
exit(0);
}
Stig Holmquist
<jdall...@yahoo.com> wrote:
>On Nov 9, 5:23�am, Stig Holmquist <stigfjor...@hotmail.com> wrote:
>> >How close to units of 7 would the mean position value be for the 6/49
>> >game and what would be the std.dev. for each?
>
>What you're asking I think, is:
>
> What is the mean and standard deviation
> for each X_i
> where (X_1, X_2, ..., X_6)
> is taken over all *sorted* combinations of
> (1,2,3,...,49}
>
>> A simulation wwith 10 million done by a friend yielded numbers very
>> close to units �of 50/7, which I guess would be the theoretical.
>
>Why "simulate" 10 million trials, when with
>14 million "trials" one can generate *all* combinations?
>
>Here's what I got:
>X_1 7.142857 sd=5.736564
>X_2 14.285714 sd=7.405872
>X_3 21.428571 sd=8.112726
>X_4 28.571429 sd=8.112726
>X_5 35.714286 sd=7.405872
>X_6 42.857143 sd=5.736564
Your means are clearly all units of 50/7 and thus it would seem
realistic to find the s.d. to related to 49 and indeed they are.
If you square the s.d. to get the variance you'll discover that for 1
and 6 the value is 32+44/49, for 2 and 5 it is 54+41.5/49 and for 3
and 4 it is 65+40/49. There must be a formula that can predict these.
A friend simulated only 1 million random sets. Thank you for data.
Stig
Stig Holmquist
wrote:
May I suggest you go to a website for the 6/49 lotto game.
James Dow Allen
> On Sun, 8 Nov 2009 18:44:28 -0800 (PST), me13013 wrote:
> >> <stigfjor...@hotmail.com> wrote:
> >> >How close to units of 7 would the mean position value be for the 6/49
> >> >game and what would be the std.dev. for each?
>
> >you mean by "mean position value". I for one have no idea what you're
> >talking about, except that it must have something to do with
> >lotteries.
>
Hi Stig!
Just a friendly note to help you on your Usenet etiquette.
*You* came *here* looking for help. Bob is trying to be helpful
(he just helped me with a *much* harder problem) and *you* tell
*him* to go look at some (unspecified!) website??
:-) :-) :-)
The suggestion was not only rude, but particularly silly,
since Bob implies he already suspects you're dealing with "lotto"
but questioned what you meant by "mean position value" -- a term
which, I'll bet, isn't even defined at your (unspecified) website.
I also found your post overly terse, confused, and confusing,
but managed to guess what you meant.
Hope this helps,
James
Colin Fairbrother
James
Stig has a fixation on Standard Deviation that goes back many years.
His latest question was raised in this thread -
http://groups.google.com/group/rec.gambling.lottery/browse_thread/thread/6df09ddc01e03991/464f679899ae2f6a#464f679899ae2f6a
As I pointed out to Stig if the draw results are presented in
numerical order then some integers will never appear in some positions
as in
1 can appear only in position 1.
2 can appear in positions 1 to 2.
3 can appear in positions 1 to 3.
4 can appear in positions 1 to 4.
5 can appear in positions 1 to 5.
6 to 44 can appear in any position.
45 can appear in positions 2 to 6.
46 can appear in positions 3 to 6.
47 can appear in positions 4 to 6.
48 can appear in positions 5 to 6
49 can appear only in position 6
The means you give reflect these numerical order constraints when
calculated on all combinations without replacement for n = 49 and k =
6.
The question I have generally thrown back at Stig is what's the good
of it? For Stig and others a look at the recent irrelevant history of
draws for a particular Lotto game with an integer showing a marked
difference to the average or SD for one of the six numerical positions
is cause to think it is more likely to occur in the next draw. You and
I know this is absolute rubbish and despite my spending considerable
time and energy demonstrating it otherwise there are some like Stig
that will never accept there is no connection.
I'll be interested to know whether what Stig reported back is a fair
reflection on your calculations or just his own interpretation?
Colin Fairbrother
me13013
> On Sun, 8 Nov 2009 18:44:28 -0800 (PST), me13013 <me13...@gmail.com>
(chuckle) Sure, you can suggest that. But I'll not be bothered to do
so.
Bob H
Mensanator
wrote:
>
> As I pointed out to Stig if the draw results are presented in
> numerical order then some integers will never appear in some positions
> as in
> 1 can appear only in position 1.
> 2 can appear in positions 1 to 2.
> 3 can appear in positions 1 to 3.
> 4 can appear in positions 1 to 4.
> 5 can appear in positions 1 to 5.
> 6 to 44 can appear in any position.
> 45 can appear in positions 2 to 6.
> 46 can appear in positions 3 to 6.
> 47 can appear in positions 4 to 6.
> 48 can appear in positions 5 to 6
> 49 can appear only in position 6
>
> The means you give reflect these numerical order constraints when
> calculated on all combinations without replacement for n = 49 and k =
> 6.
>
> The question I have generally thrown back at Stig is what's the good
> of it? For Stig and others a look at the recent irrelevant history of
> draws for a particular Lotto game with an integer showing a marked
> difference to the average or SD for one of the six numerical positions
> is cause to think it is more likely to occur in the next draw. You and
> I know this is absolute rubbish
Provided the machines are unbiased, and there have been cases of
biased
machines (sometimes deliberate on the part of the lottery operators,
and apparently accidentally). But his chances of finding such a
machine
is probably greater than the chances of winning.
me13013
Well, I just figured since she hadn't gotten any reply and it was over
24 hours since her initial post, maybe she could clarify what her post
was about. Not really anything to worry about, though.
Bob H
me13013
wrote:
> ... For Stig and others a look at the recent irrelevant history of
> draws for a particular Lotto game with an integer showing a marked
> difference to the average or SD for one of the six numerical positions
> is cause to think it is more likely to occur in the next draw. You and
> I know this is absolute rubbish and despite my spending considerable
> time and energy demonstrating it otherwise there are some like Stig
> that will never accept there is no connection.
(chuckle) On the other hand, she's also provably not making her
chances of winning any worse.
I once had the "delight" of having two co-workers just happen to be in
my office when they began an argument about this sort of thing. The
subject game was blackjack. One player kept saying "you just have to
catch the trends" and the other guy kept saying "but you can't predict
the trends" to which the first guy countered "I know you can't predict
'em, you just have to catch 'em" and so on and so on for about an
hour. I think this is much the same as arguing religion vs science.
A person believes what she believes, and no amount of logic based on
YOUR belief system can possibly change her mind, just like she can't
change yours.
Bob H
Colin Fairbrother
He is a she I think! I've often wondered though why there are not many
"shes" in Usenet groups given these days they swear just as well as
the "hes".
Regarding trends the most famous I know occurred at the Mont Carlo
casino August 18. 1913 when black came up 26 times in succession at a
roulette table. I've sometimes wondered if a mathematician happened to
be on holidays at that time would he/she have been tempted to go with
the flow or buck it after 15 blacks?
Colin
Stig Holmquist
wrote:
>On Nov 9, 11:27�am, Stig Holmquist <stigfjor...@hotmail.com> wrote:
It's not my responsibility to educate igoramuses. That would take
pages of lines. Since you don't care to inform yourself I guess there
is truth to the old saying : Ignorance is bliss. Have a good day.
Stig Holmquist
I don't play any 6/49 game and don't care about your irrelevant
jibberish.I'm only interested in the mathematical aspect. You run
a website 'Lottery Poster", which hardly anybbody respects, and ffor
good reason. If you can find any significant error besides a typo for
44/49 instead of 44.5/49 feel free to bitch and moan.
Colin Fairbrother
Colin
me13013
> On Mon, 9 Nov 2009 15:35:08 -0800 (PST), me13013 <me13...@gmail.com>
OoooKkkkkk. But are you sure you don't mean "Igorance is bliss?"
James Dow Allen
wrote:
> Regarding trends the most famous I know occurred at the Mont Carlo
> casino August 18. 1913 when black came up 26 times in succession at a
> roulette table. I've sometimes wondered if a mathematician happened to
> be on holidays at that time would he/she have been tempted to go with
> the flow or buck it after 15 blacks?
I was intriged to read at Wikipedia
http://en.wikipedia.org/wiki/Jean_le_Rond_d%27Alembert
that d'Alembert, who lived long after Pascal-Fermat developed
probability theory, apparently believed heads increase in
probability after a string of tails. This is one reason
I omit him from my List of Greatest mathematicians:
http://james.fabpedigree.com/mathmen.htm
> I'll be interested to know whether what Stig reported back is a fair
> reflection on your calculations or just his own interpretation?
I'll rerun the program, perhaps using bc, and report *exact*
rational values of the variances! Not right now though: I have
a beer date and a Go date already lined up for this afternoon.
(In that order -- I'm afraid I'll have to ask for a 4-stone
handicap.)
There's a lottery where I live. I told the ticket-sellers
I only wanted tickets with triple and quadruple numbers,
thinking that they'd hassle me else ... but they save such
special tickets for me! The only time I won (the lowest
valued prize) was holding 131313.
A few years ago this lottery was rigged. Without going
into detail, the riggers found it convenient to strive
for a number with digit repeats; I think the grand-prize
ticket was 622626 or something like that. Government
annulled that lottery round!
Thus I'm afraid my strategy (go for repeated digits because
they look pretty and you buy less often) may lead to a
*big* disappointment if/when the number hits!
James
Mensanator
:-)
Stig Holmquist
<jdall...@yahoo.com> wrote:
>On Nov 10, 7:51�am, Colin Fairbrother <colin.fairbrot...@gmail.com>
>wrote:
>> Regarding trends the most famous I know occurred at the Mont Carlo
>> casino August 18. 1913 when black came up 26 times in succession at a
>> roulette table. I've sometimes wondered if a mathematician happened to
>> be on holidays at that time would he/she have been tempted to go with
>> the flow or buck it after 15 blacks?
>
>I was intriged to read at Wikipedia
> http://en.wikipedia.org/wiki/Jean_le_Rond_d%27Alembert
>that d'Alembert, who lived long after Pascal-Fermat developed
>probability theory, apparently believed heads increase in
>probability after a string of tails. This is one reason
>I omit him from my List of Greatest mathematicians:
> http://james.fabpedigree.com/mathmen.htm
>
>> I'll be interested to know whether what Stig reported back is a fair
>> reflection on your calculations or just his own interpretation?
>
>I'll rerun the program, perhaps using bc, and report *exact*
>rational values of the variances! Not right now though: I have
>a beer date and a Go date already lined up for this afternoon.
>(In that order -- I'm afraid I'll have to ask for a 4-stone
>handicap.)
Colin was on a fishing expidition hoping to disprove my data.
You might as well have told him to wait untill Hell freezes over
before you can come up with any data to disprove mine.
I know there is a formula for predicting the means and s.d., but I
can't find it. Some time ago it was used to predict the values for the
5/55 Powerball game. Tell Colin to ask the all knowing Saliu.
Stig
James Dow Allen
wrote:
> The question I have generally thrown back at Stig is what's the good
> of it?
For the sake of argument, let's assume it's just a math exercise.
He squared the sd's I sent to conclude that the variances were
rational numbers with denominator 98. It appears he was correct.
Is there a shortcut to that result?
I wrote:
>
> What is the mean and standard deviation
> for each X_i
> where (X_1, X_2, ..., X_6)
> is taken over all *sorted* combinations of
> (1,2,3,...,49}
>
> Here's what I got:
> X_1 7.142857 sd=5.736564
> X_2 14.285714 sd=7.405872
> X_3 21.428571 sd=8.112726
> X_4 28.571429 sd=8.112726
> X_5 35.714286 sd=7.405872
> X_6 42.857143 sd=5.736564
As requested, I now show exact values for the
three distinct variances:
3 * 1075 / 98
5 * 1075 / 98
6 * 1075 / 98
These numbers seem very simple! I derived them
by brute force calculation of variance in the
obvious way. Clever shortcut is left as an
exercise. :-) :-)
James Dow Allen
Stig Holmquist
I'm glad you finally got your act together and recognized that there
is a simple pattern to the variances. Why did you not from the start
see that 0.142857 is equal to 1/7? It's elementary, Watson
Stig Holmquist
Colin Fairbrother
Stig Holmquist aka Bertil originally asked on Sun, 1 Nov 2009 in
rec.gambling.lottery the following: -
"Back in 2005 you posted "All the Worlds 649 Lottos Number Count" at
www.LottoPoster.com. Do you also have the frequencies for each integer
in
the six positions? From them one could approximate the mean.
Ideally I would like to know the theoretical mean and std.dev. for
each position. Do you know the formula for calculating them?
Stig"
(I corrected a few typos.)
The thread Stig referred to was started January 18, 2005 and is easily
found by entering the title he gave or his pseudonym Bertil and is
here along with his magic formula: -
http://lottoposter.com/forum_posts.asp?TID=90
I have now added two extra tables to this thread with the numerical
order integer occurrence per draw or combination shown in six
columns.The first table is for 20,682 draws from various Pool 49, Pick
6 Lotto games around the world. The second table is for the 13,983,816
combinations of six integers as enumerated lexicographically for a
Pool 49, Pick 6 Lotto game.
For the AllWorld649 table applying the Access Standard Deviation
function to the Line Total column a figure of 51.2034839 is given.
Colin Fairbrother
James Dow Allen
> I'm glad you finally got your act together and recognized that there
> is a simple pattern to the variances. Why did you not from the start
> see that 0.142857 is equal to 1/7? It's elementary, Watson
*Anyone* in these math groups knows at a glance that the digits .
142857
are the fractions into 7. (I suppose those digits are more well known
than the digits of pi.) I showed them at all only as a sanity check,
and avoided stating the obvious especially since you'd just given the
correct answer in the post to which I replied.
I *do* admit I didn't notice that the variances were multiplies of
1/98.
For one thing, your post didn't seem to ask for an *exact* answer.
As to who needs to get his "act together" and to understand Holmes'
advice to Watson, let me say that the calculations needed for mean
and variance are unusually trivial. Generating the lotto tickets
doesn't require Payne's algorithm but can be done with simply
for (n1 = 1; n1 < 50; n1++) /* "50" can be reduced */
for (n2 = n1+1; n2 < 50; n2++)
for (n3 = n2+1; n3 < 50; n3++)
for (n4 = n3+1; n4 < 50; n4++)
for (n5 = n4+1; n5 < 50; n5++)
for (n6 = n5+1; n6 < 50; n6++)
print(...);
(If this loop doesn't complete while you're brushing your teeth,
you must be using a computer you found in a museum!)
Obviously you're not a computer programmer, Stig, but I think
I'll use this problem as a first-day exercise next time I'm
teaching beginners. I gather from comments you've been asking
about this problem for *months*! If you'd spent the time
learning to program you'd have had your answer long ago
*and* printed "Hello, world" as well!
Hope this helps,
James Dow Allen
Stig Holmquist
<colin.fa...@gmail.com> wrote:
>James
>
>Stig Holmquist aka Bertil originally asked on Sun, 1 Nov 2009 in
>rec.gambling.lottery the following: -
>
>"Back in 2005 you posted "All the Worlds 649 Lottos Number Count" at
>www.LottoPoster.com. Do you also have the frequencies for each integer
>in
>the six positions? From them one could approximate the mean.
>Ideally I would like to know the theoretical mean and std.dev. for
>each position. Do you know the formula for calculating them?
>Stig"
>(I corrected a few typos.)
>
>The thread Stig referred to was started January 18, 2005 and is easily
>found by entering the title he gave or his pseudonym Bertil and is
>here along with his magic formula: -
>http://lottoposter.com/forum_posts.asp?TID=90
>
>I have now added two extra tables to this thread with the numerical
>order integer occurrence per draw or combination shown in six
>columns.The first table is for 20,682 draws from various Pool 49, Pick
>6 Lotto games around the world. The second table is for the 13,983,816
>combinations of six integers as enumerated lexicographically for a
>Pool 49, Pick 6 Lotto game.
>
Since you barr anybody who might disagree with you at "Lotto Poster"
I'll now attempt to illustrate a potential use for variance.
Unless I'm mistaken there is a close relationship between variance and
Chi square formula when the mean is the same. Thus I calculated the
Chi square for the 20682 draws you've tabulated. Based on the variance
and the mean I got 49.75. For 50 d.f. the value is 49.33 at 0.5.
This is close enough for practical work. You might want to do a chi
square analysis for all 49 frequencies to check my data.
I'm suggesting the same test could be done for any 6/49 game to test
for bias. Your comments are invited.Note I'm not using any stats to
pick numbers. Given the large std.dev. relative to the mean it is
futile to use any stats for picking numbers.
Stig
Stig
nigel
> I was intriged to read at Wikipedia
> http://en.wikipedia.org/wiki/Jean_le_Rond_d%27Alembert
> that d'Alembert, who lived long after Pascal-Fermat developed
> probability theory, apparently believed heads increase in
> probability after a string of tails. This is one reason
> I omit him from my List of Greatest mathematicians:
> http://james.fabpedigree.com/mathmen.htm
I googled for "croix ou pile" and d'Alambert's logic is schoolboyishly
erroneous.
I guess he didn't die rich :(
Evil Nigel
Colin Fairbrother
Contrition I guess will never be your forte. John Walker has a Chi
tester at his excellent site and an explanation in the article: -
http://fourmilab.ch/rpkp/experiments/statistics.html
After 20,682 draws there are two integers that stand out 15 with 144
below the average and 38 with 142 above.
It all comes back to what I originally stated, "The question I have
generally thrown back at Stig is what's the good of it? For Stig and
others a look at the recent irrelevant history of draws for a
particular Lotto game with an integer showing a marked difference to
the average or SD for one of the six numerical positions
is cause to think it is more likely to occur in the next draw. You and
I know this is absolute rubbish and despite my spending considerable
time and energy demonstrating it otherwise there are some like Stig
that will never accept there is no connection."
Compare that with this from Stig, "Colin was on a fishing expidition
hoping to disprove my data. You might as well have told him to wait
untill Hell freezes over before you can come up with any data to
disprove mine.I know there is a formula for predicting the means and
s.d., but I can't find it. Some time ago it was used to predict the
values for the 5/55 Powerball game. Tell Colin to ask the all knowing
Saliu."
Your membership of www.LottoPoster.com under the name Bertil is still
current and I don't recall ever deleting or moving to a hidden forum
any of your posts. I actually welcome differing viewpoints only
insisting they be rational.
Well, in Sydney as I look out the window I see a clear blue sky and
the temperature is a very pleasant 28 degrees. Looking forward to my
daily 8km walk passing by the Parramatta river this afternoon.
Colin Fairbrother
Stig Holmquist
<colin.fa...@gmail.com> wrote:
>Stig or Bertil
>
>Contrition I guess will never be your forte. John Walker has a Chi
>tester at his excellent site and an explanation in the article: -
>http://fourmilab.ch/rpkp/experiments/statistics.html
Please explain what retropsycokinesis has in common with a 6/49 lotto
game.
>
>After 20,682 draws there are two integers that stand out 15 with 144
>below the average and 38 with 142 above.
>
>It all comes back to what I originally stated, "The question I have
>generally thrown back at Stig is what's the good of it? For Stig and
>others a look at the recent irrelevant history of draws for a
>particular Lotto game with an integer showing a marked difference to
>the average or SD for one of the six numerical positions
>is cause to think it is more likely to occur in the next draw. You and
>I know this is absolute rubbish and despite my spending considerable
>time and energy demonstrating it otherwise there are some like Stig
>that will never accept there is no connection."
>
Where did you get this silly and absurd idea from? Where did I ever
mention what you claim I have proposed?
>Compare that with this from Stig, "Colin was on a fishing expidition
>hoping to disprove my data. You might as well have told him to wait
>untill Hell freezes over before you can come up with any data to
>disprove mine.I know there is a formula for predicting the means and
>s.d., but I can't find it. Some time ago it was used to predict the
>values for the 5/55 Powerball game. Tell Colin to ask the all knowing
>Saliu."
>
>Your membership of www.LottoPoster.com under the name Bertil is still
>current and I don't recall ever deleting or moving to a hidden forum
>any of your posts. I actually welcome differing viewpoints only
>insisting they be rational.
Nonsence
Stig Holmquist
I foolishly tried to comment on your new data but got this reply:
Error:" You do not have permission to reply to posts in this forum."
Who generated it? Now everybody knows what kind of person you
are. Your forum is dying because of you. You are a total shithead.
You proved that at rec.games.lottery.
Colin Fairbrother
> >>current and I don't recall ever deleting or moving to a hidden forum
> >>any of your posts. I actually welcome differing viewpoints only
> >>insisting they be rational.
>
> >Nonsence
>
> I foolishly tried to comment on your new data but got this reply:
>
> Error:" You do not have permission to reply to posts in this forum."
> Who generated it? Now everybody knows what kind of person you
> are. Your forum is dying because of you. You are a total shithead.
> You proved that at rec.games.lottery.
>
>
>
>
>
> >>Well, in Sydney as I look out the window I see a clear blue sky and
> >>the temperature is a very pleasant 28 degrees. Looking forward to my
> >>daily 8km walk passing by the Parramatta river this afternoon.
>
>
> - Show quoted text -- Hide quoted text -
>
> - Show quoted text -
I thought we were done after my last post having bothered the maths
people with enough of our Lotto nonsense. (Note the two s's Stig - I'm
usually not picky about spelling as long as I get the general drift -
everyone make typos - however, apart from the dyslexic ones, others
can give an indication of ones general education especially if English
is your mother tongue. In your case I suggest you use the spelling
check that is standard with Internet Explorer if you want to hide your
handicap for a while. However, after a sentence or two most would
conclude to use the vernacular that you are not a full quid. I have
read stuff you have posted on various forums mostly to do with your
fixation on Standard Deviation since 2004 and decided to be kind to
you taking into consideration that you may have fallen on your head or
suffered some other unfortunate accident that jellified part of your
"brain" in your infancy.)
The reason you got that message Stig is because you have to log in
under the name Bertil and it is generatied by ASP code not by me
monitoring personally everyone that goes to the site. The login form
appeared underneath the message you refer to. If you have forgotten
your password then at the login page you can ask for it to be emailed
to you. Here is the login page: -
http://lottoposter.com/login_user.asp?FID=0
Please don't bother telling me that you wouldn't consider logging in
under any circumstances. I don't care Stig. In the general oder of
things I don't have any misgivings in stepping on an ant and you rank
somewhere below that.
I'm done here Stig. My apologies to the regulars of this group if not
amused by all this drivel. If you got a laugh or at least a smile,
well, maybe that will help you live longer.
Toodle Oo
Colin Fairbrother
Henry
> On Sun, 8 Nov 2009 22:40:07 -0800 (PST), James Dow Allen
> >Here's what I got:
> >X_1 7.142857 sd=5.736564
> >X_2 14.285714 sd=7.405872
> >X_3 21.428571 sd=8.112726
> >X_4 28.571429 sd=8.112726
> >X_5 35.714286 sd=7.405872
> >X_6 42.857143 sd=5.736564
>
> realistic to find the s.d. to related to 49 and indeed they are.
> If you square the s.d. to get the variance you'll discover that for 1
> and 6 the value is 32+44/49, for 2 and 5 it is 54+41.5/49 and for 3
> and 4 it is 65+40/49. There must be a formula that can predict these.
OK, let's find a formula:
With k numbers from 1,2,3,...,n
Prob(X_i=r) = C(r-1;i-1) * C(n-r;k-i) / C(n,k)
E[X_i] = sum_r Prob(X_i=r) * r
= i * (n+1) / (k+1)
Var[X_i] = sum_r Prob(X_i=r) * r^2 - E[X_i]^2
= i * (k-i+1) * (n-k) * (n+1) / ( (k+2) * (k+1)^2 )
So taking n=49, k=6 and i=2 we would get
E[X_2] = 2*50/7 = 100/7 = 14.2857...
Var[X_2] = 2*5*43*50/(8*7*7) = 5375/98 = 54.8469...
sd[X_2] = sqrt(5375/98) = 7.40587...
as in JDA's table
Stig Holmquist
wrote:
Yes, you've got it. The same formula has been derived by a friend.
Now Saliu can claim he knew it all along.
Stig