1. ## Quick Notation Question

I had to miss class today due to another engagement and in learning what I missed on Bivariate Probability Distributions I've come across this notation.

$f_{XY}(x,y)$

Is this another notation for a function of two variables or does it denote partial derivatives?

$f_{XY}(x,y)=f(x,y)$?
or
$f_{XY}(x,y)=\frac{d}{dx}\frac{d}{dy}f(x,y)$?

Or something else?

Thanks for the clarification!

Kasper

2. $f_{XY}(x,y)$ denotes the joint probability distribution of two continuous random variables X and Y.

3. Originally Posted by harish21
$f_{XY}(x,y)$ denotes the joint probability distribution of two continuous random variables X and Y.
Oh, k. Thanks!

4. These are not partial derivatives.
We use the subscripts since one bivariate density generates 4 more densities, the two marginals and the two conditionals.
Thus, there are five densities and we use f for all five.
The subscripts "differentiates" an excellent pun, which density is which.
BUT there is no differentiation here at all.
NOW, f is the derivative of F, the cdf........