The numbers I sent are experimental results. But it's easy to show that if one picks three numbers at random, the probability that the third will be greater (smaller) than the other two is 1/3. The argument is similar to the argument about the middle number.
For any three numbers one of them must be the largest -- assuming that we are not allowing two of them to be equal. Each of the three numbers has an equal chance of being that largest number. Hence the third number has a 1/3 chance. Similarly it has a 1/3 chance of being the smallest. Is that too facile an argument? Is there a mathematician out there who can say whether that is sufficient? *-- Russ* On Sat, Jun 11, 2011 at 12:43 PM, joseph spinden <[email protected]> wrote: > Is that an experimental result, or what you think it should be ? > > Joe > > > > > > On 6/10/11 11:42 PM, Russ Abbott wrote: > > Right. Each is about 333. > > *-- Russ Abbott* > *_____________________________________________* > * Professor, Computer Science* > * California State University, Los Angeles* > > * Google voice: 747-*999-5105 > * blog: *http://russabbott.blogspot.com/ > vita: http://sites.google.com/site/russabbott/ > *_____________________________________________* > > > > On Fri, Jun 10, 2011 at 8:03 PM, joseph spinden <[email protected]> wrote: > >> x <- runif(1000) # generate 1000 random numbers from a uniform distribution >> y <- runif(1000) # generate 1000 random numbers from a uniform distribution >> z <- runif(1000) # generate 1000 random numbers from a uniform distribution >> >> A <- y < pmin(x, z) >> B <- y > pmax(x, z) >> >> print(sum(A)) >> >> print(sum(B)) >> >> > > -- > > "Sunlight is the best disinfectant." > > -- Supreme Court Justice Louis D. Brandeis, 1913. > >
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