Question

求Dξ= Eξ^2 - (Eξ)^2

Answer 1

DX=E(X-EX)^2【这是定义】=E(X^2-2X*EX+(EX)^2)=E(X^2)-2E(X*EX)+E[(EX)^2]=E(X^2)-2(EX)^2+(EX)^2=E(X^2)-(EX)^2

请注意EX为一个常数,故E(X*EX)= (EX)^2 [常数可提到期望外]