Re: Independent Random Variables

On 6 Apr 2007 16:47:47 -0700, albert.koltai@xxxxxxxxx wrote:


I am now taking a course in Probability Theory, and I am having
trouble "visualizing" what do two independent random variables look
like. The definition in terms of the cumulative distribution function
or in terms of probability densities is clear enough, but when I am
trying to imagine say, two or more real valued independent variables
defined on the reals (with Borel sets as the sigma alegbra) I am
drawing a blank.

Could someone give me nontrivial examples of a set of real valued
defined of the reals independent random variables?
A general method of obtaining such -- nice enough to graph them --
random variables would be better.

I once read in some book that the notion of "independent variables"
in probability has nothing to do with the "independent variables"
that you find in calculus books. That was a lie - the two concepts
are very closely related.

Assuming that you're talking about probability theory based
on measure theory: Two random variables X and Y are independent
if and only if the sample space can be realized as a _product_
space, where the distribution of X is a measure depending only
on one variable and the distribution of Y is a measure depending
only on the other variable.

Thank you,
Albert


************************

David C. Ullrich
.

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