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 2010-04-29, 16:23 #1 henryzz Just call me Henry     "David" Sep 2007 Cambridge (GMT/BST) 2·3·7·137 Posts Coin tossing 2 Here is another look at coin tossing. Which of these three strings is most likely to have been produced by 32 tosses of a coin and not constructed manually? Can anyone come up with some statistics to verify that? a) THHTHTHTHTHTHTHTHTTTHTHTHTHTHTHH b) THHTHTHTHHTHTHHHTTHHTHTTHHHTHTTT c) TTHTTHHTHHTTTTTHTTHHTTHTTTTTTHTH
2010-04-29, 16:53   #2
rogue

"Mark"
Apr 2003
Between here and the

2×3,023 Posts

Quote:
 Originally Posted by henryzz Here is another look at coin tossing. Which of these three strings is most likely to have been produced by 32 tosses of a coin and not constructed manually? Can anyone come up with some statistics to verify that? a) THHTHTHTHTHTHTHTHTTTHTHTHTHTHTHH b) THHTHTHTHHTHTHHHTTHHTHTTHHHTHTTT c) TTHTTHHTHHTTTTTHTTHHTTHTTTTTTHTH
They are all equally probable.

Last fiddled with by rogue on 2010-04-29 at 16:53

 2010-04-29, 16:55 #3 10metreh     Nov 2008 2·33·43 Posts Each one has a 1/232 chance of being produced by 32 tosses of a coin. Thus none of them is more likely than the others to appear. C is the one that most *resembles* the majority of 32-toss sequences.
 2010-04-29, 18:55 #4 henryzz Just call me Henry     "David" Sep 2007 Cambridge (GMT/BST) 2·3·7·137 Posts I was hoping someone wouldn't come up with that answer. Try this: How probable is it that in a sequence of 32 tosses you would get runs of heads or tails of length r? Then which do you think was not created manually. Last fiddled with by henryzz on 2010-04-29 at 18:55
2010-04-29, 22:06   #5
RichD

Sep 2008
Kansas

C6F16 Posts

Quote:
 Originally Posted by henryzz How probable is it that in a sequence of 32 tosses you would get runs of heads or tails of length r?
Do you mean at least a run of r or exactly r?

The exactly r would be much more difficult since that means the one before the first toss of the run must be the "other" side and the one immediately after the run must also be the "other" side.

But there is a slight bonus if the run starts at toss 1 or ends at toss 32.

Any takers?

2010-04-30, 16:59   #6
henryzz
Just call me Henry

"David"
Sep 2007
Cambridge (GMT/BST)

2×3×7×137 Posts

Quote:
 Originally Posted by RichD Do you mean at least a run of r or exactly r? The exactly r would be much more difficult since that means the one before the first toss of the run must be the "other" side and the one immediately after the run must also be the "other" side. But there is a slight bonus if the run starts at toss 1 or ends at toss 32. Any takers?
Don't mind which. If we solve the easy one though it would be worth trying the harder.

 2010-05-13, 01:46 #7 __HRB__     Dec 2008 Boycotting the Soapbox 24×32×5 Posts I think what henryzz wants to hear, is that since we expect N/2 runs of length 1, N/4 runs of length 2,...,N/2^k runs of length k, we could use chi-square to generate confidence intervals. A really cheap test could actually be to simply count runs R, because then some expression like (N-R-1)/(N-2) should be t-distributed.
2010-05-13, 02:55   #8
davieddy

"Lucan"
Dec 2006
England

194A16 Posts

Quote:
 Originally Posted by __HRB__ we expect N/2 runs of length 1, N/4 runs of length 2,...,N/2^k runs of length k
May have too much blood in my alcohol stream ATM, but

1/2 + 2/4 + .. k/2^k +.... = 2

?

Sundance

2010-05-13, 04:05   #9
__HRB__

Dec 2008
Boycotting the Soapbox

24·32·5 Posts

Quote:
 Originally Posted by __HRB__ A really cheap test could actually be to simply count runs R, because then some expression like (N-R-1)/(N-2) should be t-distributed.
OK, apparently the expressions are a little more complicated. According to:

https://pantherfile.uwm.edu/ericskey...L29/node2.html

If we let R denote the number of runs, H the number of Heads and T the number of Tails, then

E[R]=2*H*T/(H+T)+1

and

VAR[R]=2*H*T*(2*H*T-H-T)/[(H+T)^2*(H+T-1)]

and the standardized number of runs is asymptotically normal distributed. In any case, smaller standardized values should be considered 'preferred by henryzz'. I'm too lazy to plug in the actual numbers to give a definite answer.

Quote:
 Originally Posted by davieddy May have too much blood in my alcohol stream ATM, but 1/2 + 2/4 + .. k/2^k +.... = 2 ? Sundance
Cheers!

Butch

Last fiddled with by __HRB__ on 2010-05-13 at 04:16

2010-05-14, 00:47   #10
Orgasmic Troll
Cranksta Rap Ayatollah

Jul 2003

641 Posts

Quote:
 Originally Posted by henryzz Here is another look at coin tossing. Which of these three strings is most likely to have been produced by 32 tosses of a coin and not constructed manually? Can anyone come up with some statistics to verify that? a) THHTHTHTHTHTHTHTHTTTHTHTHTHTHTHH b) THHTHTHTHHTHTHHHTTHHTHTTHHHTHTTT c) TTHTTHHTHHTTTTTHTTHHTTHTTTTTTHTH
just at a glance, C

 2010-05-14, 11:21 #11 davieddy     "Lucan" Dec 2006 England 11001010010102 Posts With the greatest (lack of) respect, have any of you ever considered why nCr = n!/((n-r)!*r!) ? Or even glanced at the "coin tossing" thread? David Or heard of the binomial theorem, let alone the binomial distribution? Last fiddled with by davieddy on 2010-05-14 at 11:41

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