设随机变量X1,X2,X3相互独立,且则E[X1(X1+X2-X3)]为___________.

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问题 设随机变量X1,X2,X3相互独立,且则E[X1(X1+X2-X3)]为___________.

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答案[*]

解析 E[X1(X1+X2—X3)]=E(X12+X1X2一X1X3)=E(X12)+E(X1)E(X2)一E(X1)E(X3)=D(X1)+[E(X1)]2+E(X1)E(X2)一E(X1)E(X3)
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