Functions of Multiple Random Variables

Definition

• Suppose RV $X,Y$
• Suppose we define two transformations $Z,W$ For one function: $\left[\begin{array}{c}X\\ Y\end{array}\right]⟹Z=h(X,Y)$ For two functions merging into one function: $\left[\begin{array}{c}X\\ Y\end{array}\right]⟹\left[\begin{array}{c}Z\\ W\end{array}\right]=\left[\begin{array}{c}{h}_1(X,Y)\\ h_2(X,Y)\end{array}\right]=h(X,Y)$