PMF Method for Deriving Distribution for Multivariable Transformation

Method

• For Discrete RV $X,Y$
• For Joint PMF $p_{X,Y}(x,y)$
• To calculate Joint PMF $Z=h_1(X,Y),W=h_2(X,Y)$ $p_{Z,W}=P(Z=z,W=w)={\sum }_{(x,y)\in h_{-1}}{p}_{X,Y}(x,y)$