2D Lotus

Theorem

Discrete

• Let g be a function from $R^2$ to $R$. If X and Y are discrete, then: $E(g(X,Y))={\sum }_x{\sum }_{y}g(x,y)P(X=x,Y=y)$

Continuous

• If X and Y are continuous with a joint PDF fx,y then: $E(g(X,Y))={\int }_{-\infty }^{\infty }{\int }_{-\infty }^{\infty }g(x,y)f_{X,Y}dxdy$

Example