Question

设随机变量X,Y相互独立，且E(X)=E(Y)=1，D(X)=2，D(Y)=3，求：(1)E(X2),E(Y2);(2)D(XY).

Answer 1

【答案】：(1)E(X²)=D(X)+(E(X))²=2+1=3.
E(Y²)=D(Y)+(E(Y))²=3+1=4.
(2) D(XY)=E(X²Y²)-(E(XY))²=E(X²)E(Y²)-(E(X)·E(Y))²=[D(X)+(E(X))2][D(Y)+(E(Y))²]-[E(X)]²[E(Y)]²=3×4-1×1=11