Re: Probability question

Hello Robert,

I think that if X<=Y almost sure, then P(X<=Z)>=P(Y<=Z) will hold for
every random variable Z. Thanks.

Wing


Robert Israel wrote:

> In article <1128259580.415900.73910@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
> Wing <nilland@xxxxxxxxxxxxx> wrote:
> >Let X and Y be random variable. Assume we know that P(X<=a)>=P(Y<=a)
> >for any real number "a".
> >
> >Can we conclude that P(X<=Z)>=P(Y<=Z) for any random variable Z?
>
> No. E.g. let X and Y be the results of independent rolls of a die,
> Z = { X + 1 if X <= 5,
> { 1 if X = 6.
>
> Robert Israel israel@xxxxxxxxxxx
> Department of Mathematics http://www.math.ubc.ca/~israel
> University of British Columbia Vancouver, BC, Canada

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