怎么证明E(Xi^2)=D(Xi)+E(Xi)^2

问题描述:

怎么证明E(Xi^2)=D(Xi)+E(Xi)^2

D(Xi) = E[(Xi - E(Xi))^2] = E(Xi^2 - 2 Xi E(Xi) + E(Xi)^2)= E(Xi^2) - 2E(Xi E(Xi)) + E(E(Xi)^2)= E(Xi^2) - 2E(Xi)E(Xi)+E(Xi)^2= E(Xi^2) - E(Xi)^2,故E(Xi^2)=D(Xi)+E(Xi)^2.