设随机变量X~P(λ),且E[(X一1)(X一2)]=1,则λ=___________.

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问题 设随机变量X~P(λ),且E[(X一1)(X一2)]=1,则λ=___________.

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答案1

解析 因为X~P(λ),所以E(X)=λ,D(X)=λ,故E(X2)=D(X)+[E(X)]22+λ.
  由E[(X一1)(X一2)]=E(X2一3X+2)=E(X)一3E(X)+2=λ2一2λ+2=1得λ=1.
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