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-X1X3)
=E(X12)+EX1EX2-EX1EX3
=DX1+(EX1)2+EX1EX2-EX1EX3
=
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