Joint pdf for two CONTINUOUS random variables

Joint pdf for two CONTINUOUS random variables

Def. Let X and Y be continuous random variables. Then f (x,y) is the joint probability density function for X and Y if for a any two-dimensional set A P [(x,y)  A ] = In particular, if A is the two-dimensional rectangle {(x,y) : a  x  b, c  y  d}, then P[(X,Y)  A] = P (a  X  b, c  Y  d) =

Note f (x,y) is a joint pdf if: f (x,y)  0

= 1