Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: say I flip a coin 100 times...
Replies: 46   Last Post: Apr 18, 2005 9:42 PM

 Messages: [ Previous | Next ]
 tchow@lsa.umich.edu Posts: 1,133 Registered: 12/6/04
Re: say I flip a coin 100 times...
Posted: Apr 15, 2005 12:05 PM

In article <425fc441\$0\$563\$b45e6eb0@senator-bedfellow.mit.edu>, I wrote:
> (probability of a complete match) * (length of a complete match).
>
>The probability of a complete match is zero, and the length of a complete
>match is infinite. There isn't a good way of defining 0 * infinity,
>so the expected value is undefined.

Sorry, I should have thought this problem through more carefully before
posting.

Suppose that in comparing Herc's sequence with the other sequence, I find
that for every *finite* prefix, there is someone who shares that finite
prefix with Herc, but there is nobody whose sequence matches Herc's
*completely*. Then we need to decide what the "length of the longest
matching prefix" should be defined to be in this case. If we define it
to be infinite, then the expected value comes out to be infinite.

But of course, this doesn't mean that Herc's sequence matches someone
else's sequence exactly with probability 1. That probability is still 0.
--
Tim Chow tchow-at-alum-dot-mit-dot-edu
The range of our projectiles---even ... the artillery---however great, will
never exceed four of those miles of which as many thousand separate us from
the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences

Date Subject Author
4/12/05 HERC777
4/12/05 Jan Burse
4/12/05 HERC777
4/12/05 George Greene
4/13/05 Glenn C. Rhoads
4/13/05 Barb Knox
4/13/05 HERC777
4/13/05 Yajun
4/13/05 HERC777
4/13/05 Jay
4/13/05 HERC777
4/13/05 Jay
4/14/05 Yajun
4/14/05 George Greene
4/14/05 George Greene
4/13/05 Will Twentyman
4/13/05 briggs@encompasserve.org
4/13/05 briggs@encompasserve.org
4/14/05 George Greene
4/14/05 tchow@lsa.umich.edu
4/14/05 briggs@encompasserve.org
4/12/05 Tony
4/13/05 HERC777
4/13/05 ken quirici
4/13/05 Ralph Hartley
4/13/05 Robert Low
4/13/05 Ralph Hartley
4/13/05 Robert Low
4/13/05 tchow@lsa.umich.edu
4/13/05 HERC777
4/13/05 tchow@lsa.umich.edu
4/14/05 HERC777
4/14/05 George Greene
4/14/05 HERC777
4/15/05 tchow@lsa.umich.edu
4/15/05 tchow@lsa.umich.edu
4/16/05 George Greene
4/16/05 HERC777
4/17/05 George Greene
4/17/05 Patricia Shanahan
4/17/05 HERC777
4/18/05 Patricia Shanahan
4/17/05 tchow@lsa.umich.edu
4/18/05 HERC777
4/18/05 George Greene
4/18/05 tchow@lsa.umich.edu
4/18/05 HERC777