已知随机变量X与Y的联合概率分布为 又P{X+Y=1}=0.4,则α=__________;β=__________;P{X+Y<1}=__________;P{X2Y2=1} =__________.

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问题 已知随机变量X与Y的联合概率分布为

又P{X+Y=1}=0.4,则α=__________;β=__________;P{X+Y<1}=__________;P{X2Y2=1} =__________.

选项

答案0.3 0.1 0.4 0.3

解析 由0.1+0.2+α+β+0.1+0.2=1
及    P{X+Y=1}=p{X=0,Y=1}+P{X=1,Y=0}=α+0.1=0.4
解得α=0.3,β=0.1.于是
P{X+y<1}=P{x=i,y=j}
=P{X=0,Y=-1}+P{X=0,Y=0}+P{X=1,Y=-1}
=0.1+0.2+0.1=0.4;
P{X2Y2=1}=P{X=1,Y=-1}+P{X=1,Y=1}=0.1+0.2=0.3.
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