Theorem:IfXandYare two independent and continuous random variables with pdf’s f(x) and g(y) respectively, then the sumU = X + Yis a continuous random variable with pdf given by .

Theorem:IfXandYare two independent and continuous random variables with pdf’s f(x) and g(y) respectively and Pr(X = 0) = Pr(Y = 0) = 0, then the productU = XYis a continuous random variable with pdf given by .