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From: Randy Poe <poespam-trap@yahoo.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Calculating cumulative probability
Date: Thu, 14 Feb 2008 08:42:50 -0800 (PST)
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On Feb 14, 11:35 am, "Omkar Palsule-Desai" <omkar...@iimahd.ernet.in>
wrote:
> Hi,
>
> Say, X & Y are two independent continuous random variables
> with known distribution functions. Both X & Y range on (-
> inf, +inf). I need to find following probability
>
> (X-Y<= k; Y>=0; X>Y)
>
> Since, I have two random variables and there are three
> conditions in joint distribution, I can not use
> traditional probability concepts.

What?

This isn't a conditional probability as you stated it.
You defined three "events", and you are asking for
the probability of (A and B and C). These events
are dependent. There is nothing in traditional probability
theory that prevents you from considering the concept
P(A and B and C).

> I guess I can calculate probability by measuring volume
> under the surfaces defined by X-Y<=k, Y>=0 and X>Y. Is
> this a correct procedure?

Yes. The covers the region of (X,Y) where (A and B and C)
is true, and the integral of the density over that region
is the probability of (A and B and C).

> If it is, then how do I calculate the volume using matlab?

Numerically or symbolically?

Draw the region defined by these three conditions on
an x-y axis (on paper). See if you can express that as
a double integral over x and y. That will give you limits
which you can use in an integration routine, either numeric
(like quad2) or symbolic (I'm not very knowledgable about
that).

                - Randy