Comments on: Probability of long runs http://www.johndcook.com/blog/2012/11/14/probability-of-long-runs/ John D. Cook Wed, 22 May 2013 00:05:53 +0000 hourly 1 http://wordpress.org/?v=3.5.1 By: Douglas Zare http://www.johndcook.com/blog/2012/11/14/probability-of-long-runs/comment-page-1/#comment-22189 Douglas Zare Thu, 28 Mar 2013 17:00:32 +0000 http://www.johndcook.com/blog/?p=12448#comment-22189 Hi. Someone linked to this post from http://mathoverflow.net/questions/125814/maximal-chain-of-1s-in-binary-strings. I have a few comments.

In the motivating statistical experiment, it may make sense to choose the assignments in a more balanced fashion than assigning individuals independently. For example, if there are 10 subjects, you might choose randomly from among the ways to assign 5 to each treatment rather than risking the assignment of 9/10 to treatment A by luck.

The formula you give for the standard deviation differs from the one in Schilling’s papers by a factor of pi/sqrt(6).

The distribution about the mean is not normal. The tails drop off only roughly exponentially (for a while).

]]> By: ezra abrams http://www.johndcook.com/blog/2012/11/14/probability-of-long-runs/comment-page-1/#comment-3486 ezra abrams Sat, 17 Nov 2012 00:57:12 +0000 http://www.johndcook.com/blog/?p=12448#comment-3486 thanks
if there were a collection of 100 surprising math facts about the real world every scientists and engineer should know, this would surely be on the list.

]]> By: A Confused One http://www.johndcook.com/blog/2012/11/14/probability-of-long-runs/comment-page-1/#comment-3485 A Confused One Thu, 15 Nov 2012 19:00:07 +0000 http://www.johndcook.com/blog/?p=12448#comment-3485 Thanks you for your explanation – and the follow-up post :) .

]]> By: John http://www.johndcook.com/blog/2012/11/14/probability-of-long-runs/comment-page-1/#comment-3484 John Thu, 15 Nov 2012 11:17:16 +0000 http://www.johndcook.com/blog/?p=12448#comment-3484 When I write “log,” I always mean natural log.

]]> By: A Confused One http://www.johndcook.com/blog/2012/11/14/probability-of-long-runs/comment-page-1/#comment-3483 A Confused One Thu, 15 Nov 2012 06:34:46 +0000 http://www.johndcook.com/blog/?p=12448#comment-3483 My python says 1/m.log10(1/0.5) 3.321928094887362, but math.log means ln. So what’s the base of your log? 10, e, 2?

]]> By: Luis Mendo http://www.johndcook.com/blog/2012/11/14/probability-of-long-runs/comment-page-1/#comment-3482 Luis Mendo Wed, 14 Nov 2012 15:43:07 +0000 http://www.johndcook.com/blog/?p=12448#comment-3482 Whoops, I didn’t see that! Thanks

]]> By: John http://www.johndcook.com/blog/2012/11/14/probability-of-long-runs/comment-page-1/#comment-3481 John Wed, 14 Nov 2012 15:35:51 +0000 http://www.johndcook.com/blog/?p=12448#comment-3481 Luis: Please see the paper by Mark F. Schilling in the last line of the post.

]]> By: Luis Mendo http://www.johndcook.com/blog/2012/11/14/probability-of-long-runs/comment-page-1/#comment-3480 Luis Mendo Wed, 14 Nov 2012 15:27:14 +0000 http://www.johndcook.com/blog/?p=12448#comment-3480 Could you provide a reference for the expression of the expected length of the longest run? I would like to read more on that. Thanks!

]]> By: Dr. Drang http://www.johndcook.com/blog/2012/11/14/probability-of-long-runs/comment-page-1/#comment-3479 Dr. Drang Wed, 14 Nov 2012 14:29:08 +0000 http://www.johndcook.com/blog/?p=12448#comment-3479 A few years ago, Radiolab had an episode called Stochasticity, in which they talked about the likelihood of seemingly unlikely events. One of the examples was a run of seven tails in sequence of 100 coin flips. I wrote a post about how to calculate the probability of such runs, which involves k-step Fibonacci numbers, but never considered the statistics of the longest run. It’s fun to see a different (and, frankly, much simpler) way of looking at the problem.

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