Expected Value of Function

Univariate

• For a given RV $X$
• For a given function $Y=g(X)$
• Then, $E(Y)={\sum }_y^{}g(x)p_X(x)=E(g(X))$

Multivariate

• For given RV $X,Y$
• For a given function $Z=g(X,Y)$
• $E[Z]=E[g(X,Y)]={\sum }_n^{}{\sum }_y^{}g(x,y)P(X=x,Y=y)$