Re: probability = 1/infinite ?


Roy wrote:
> Thank you very much.
> However, intuitively, it seems each outcome of x is equally likely to
> be mapped to k for the product.
> Is there any way to prove such claim? Assume random variable y has a
> uniform distribution in R.

There is no such thing as a uniform distribution on the whole real
line.
You could take the next-best thing as a sequence of distributions that
approach uniformity in the sense that the ratios of densities
f(a)/f(b) -> 1 for every a and b. But if you take such a sequence of
distributions for Y, the corresponding distributions for X will not
approach uniformity.

If Y has a distribution with density f_Y, then X = k/Y has density
f_X(x) = k/x^2 f_Y(k/x). So if f_Y(a)/f_Y(b) -> 1 for every a and b,
f_X(a)/f_X(b) -> b^2/a^2.

Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada

.

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