Question

证明：概率论问题[E(ZY)]^2<=E(Z^2)*E(Y^2)

Z,Y,E(Z^2),E(Y^2)均存在。

Answer 1

E(X+tY)^2=(EY^2)t^2+(2EXY)t+EX^2≥0
△=(2EXY)^2-4*(EY^2)*(EX^2)≤0
即得：[E(XY)]^2<=E(X^2)*E(Y^2)