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

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问题 设随机变量X~P(λ),且E[(X-1)(X-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)]2=λ2+λ.
由E[(X-1)(X-2)]=E(X2-3X+2)=E(X2)-3E(X)+2=λ2-2λ+2=1得λ=1.
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