Perhaps I was not clear. I wondered if the 333 was an "experimental"
result, since you had previously listed 11 "experimental" results, none
of which was 333.
In any case, I agree the probability is 1/3, as long as you are randomly
sampling from a uniform distribution. Given your program, it would have
been surprising if the "experimental" results did not approximate 1/3.
But that is due to the program. I do not understand why you think the
program illustrates a stopping rule or strategy.
Perhaps if you stated the stopping rule or strategy explicitly in terms
of your program, it would be clearer to me.
Joe
On 6/11/11 7:32 PM, Russ Abbott wrote:
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]
<mailto:[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]
<mailto:[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.
--
"Sunlight is the best disinfectant."
-- Supreme Court Justice Louis D. Brandeis, 1913.
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