0 Office_Shredder said (xy) 2 = x 2 2xy y 2 >= 0 You know that already So x 2 xy y 2 >= xy If x and y are both positive, the result is trivial If x and y are both negative, the result is also trivial (in both cases, each term in the summation is positive) When one of x or y is negative, xy becomes positive4 solve xy' y = sqrt(x^2 y^2) 5 solve the following second order differential equation with constant coefficients y" 7y' 12y = 12x 19 initial conditions y(0) = 3 ;Covariance term appears in that formula Var(X Y) = Var(X) Var(Y) 2Cov(X;Y) Here's the proof Var(X Y) = E((X Y)2) E(X Y) = E(X2 2XY Y2) 2( X Y) = E(X2) 2E(XY) E(Y2) 2 X 2 X Y 2 Y = E(X2) 2 X 2(E(XY) X Y) E(Y2) 2 = Var(X) 2Cov(X;Y) Var(Y) Bilinearity of covariance Covariance is linear in each coordinate That means
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