设X~N(1,4),Y~B(3,)且X,Y相互独立,则P{XY+1>X+Y}=___________.

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问题 设X~N(1,4),Y~B(3,)且X,Y相互独立,则P{XY+1>X+Y}=___________.

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答案[*]

解析 P{XY+1>X+Y}=P{(X一1)(Y一1)>0}
    =P{X>1,y>1}|{P{X<1,y<1}
    =P{X>1}P{y>1}+P(X<1}P{y<1}
   
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