I'm having a problem evaluating a distribution-(adsbygoogle = window.adsbygoogle || []).push({});

Suppose X and Y are Chi-square random variables, and a is some

constant greater than 0. X and Y are independent, but not identically distributed (they have different DOFs).

I want to find

P(X>a,X-Y>0). So I use Bayes' theorem to write

P(X>a,X-Y>0)

=P(X>a | X-Y > 0)*P(X-Y>0)

=P(X>a| X>Y)*P(X>Y)

Now I have an expression for P(X>a) and P(X>Y), but I am at a

loss as to how to evaluate the conditional distribution P(X>a|

X>Y).

I figured out that if Y was a constant (rather than a random variable), then I could write

P(X>a| X>Y) = { 1 if Y>a

{ P(X>a)/P(X>Y) if Y<a

But this does not help evalaute the distribution because I requires knowledge of the value of random variable Y.

I also tried to write

P(X>a,X-Y>0)

=P(X-Y > 0|X>a)*P(X>a)

=P(X>Y| X>a)*P(X>a)

So to evaluate P(X>Y| X>a) I write

P(X>Y| X>a) = int(a...inf (int(0...x f_XY)) dYdX

But this gives some ugly expression which I cannot relate to simply P(X>Y) or P(X>a)

Any help will be much appreciated.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Joint/Conditional distribution

Can you offer guidance or do you also need help?

**Physics Forums | Science Articles, Homework Help, Discussion**