Re: Probability in an infinite sample space




Gerry Myerson wrote:
In article <1143081361.594441.272290@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mzafrullah@xxxxxxx wrote:

You are the expert. In this case I see naturals split into steps of
three and that, even though the set of natural numbers is infinite, any
natural number that you pick is finite and so it falls at the left end,
right end or the middle of one of these steps, with obviously equal
probability.

If it's obvious to you that these probabilities are equal,
then it must also be obvious to you what the probability is
that the number you pick is 42. So, what is that probability?

--
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for email)

If you are serious the probability is zero because the sample space
here is infinite. If you wanna go the hitch-hikers' way the probability
of picking 42 is the same as the probability of picking the number that
results on computing 9x6. (You probably missed out "in this case
above".)
Muhammad

.



Relevant Pages

  • Re: Calculus XOR Probability
    ... If one of the elements is to be chosen from the set, then the probability of one being chosen is 1. ... then that 1 representing the fact that one of those will be chosen is defined to be the sum of the probabilities of each. ... If you can establish a uniform probability distribution, then you can say each possibility has the same probability. ... If we are discussing an infinite set of possiblities, and I define infinitesimal in terms of that infinity, it's not circular. ...
    (sci.math)
  • Re: Calculus XOR Probability
    ... the sum of a countable number of 0's; he simply "wants" it to be 1. ... then the probability of one being chosen is 1. ... the question is why the standard system can't accomodate the infinite case, ... The probability of each is 0 in standard analysis, ...
    (sci.math)
  • Re: Calculus XOR Probability
    ... therefore there must exist a uniform distribution on the naturals. ... If you use a 2 element set, you still get a total probability of 1. ... the sum of a countable number of 0's; he simply "wants" it to be 1. ... the question is why the standard system can't accomodate the infinite case, ...
    (sci.math)
  • Re: Calculus XOR Probability
    ... If one of the elements is to be chosen from the set, then the probability of one being chosen is 1. ... then that 1 representing the fact that one of those will be chosen is defined to be the sum of the probabilities of each. ... If you can establish a uniform probability distribution, then you can say each possibility has the same probability. ... If we are discussing an infinite set of possiblities, and I define infinitesimal in terms of that infinity, it's not circular. ...
    (sci.math)
  • Re: Cantorian pseudomathematics
    ... > Tony Orlow wrote: ... The probability ... >> of picking any particular one is essentially 0, ... countably infinite set. ...
    (sci.math)