# Math Help - Covariances

1. ## Covariances

Let X1, X2, Y1 and Y2 be random variables.
(a) Show that Cov(X1 +X2, Y1 +Y2) = Cov(X1, Y1)+Cov(X1, Y2)+
Cov(X2, Y1) + Cov(X2, Y2)

Please walk me through how to solve the question.

2. Originally Posted by loveandpeace
Let X1, X2, Y1 and Y2 be random variables.
(a) Show that Cov(X1 +X2, Y1 +Y2) = Cov(X1, Y1)+Cov(X1, Y2)+
Cov(X2, Y1) + Cov(X2, Y2)

Please walk me through how to solve the question.
I'd start by letting U = X1 + X2 and W = Y1 + Y2 and then use the usual definition to find Cov(U, V).