Re: Probability of picking a positive rational number at random
- From: Tim Little <tim@xxxxxxxxxxxxxxxxxxxxxxxxxx>
- Date: Fri, 14 Mar 2008 08:57:07 -0000
On 2008-03-13, S_Paske@xxxxxxxxxxx <S_Paske@xxxxxxxxxxx> wrote:
From my understanding, the probability of picking a positive
rational number at random which is <1 is 50%
First you have to decide what you mean by "picking a positive rational
number at random". What distribution will you use?
One possibility is to pick any probability distribution p(n) over
positive integers, and let
p_Q(q) = Sum_{x,y in N with x = q y} p(x) p(y).
This ensures that for any s,r in N, p_Q(r/s) = p_Q(s/r), so it is
"nicely" symmetric, but won't ever have p_Q(1) = 0. And there is
still lots of freedom in what distribution you choose over the
positive integers.
What is the probability that the number is <1/2. What about <2?
How about <1/3 or < 3?
Mostly up to you - pick some numbers. Though I do recommend that
whenever A is less than B, you assign P(x < A) <= P(x < B).
- Tim
.
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