概率论联合分布函数问题

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(1)由0.2+0.3+a+0.1+0.1+0.1=1可知,a=0.2
X的边缘概率分布为
P(X=-1)=P(X=-1, Y=0)+P(X=-1, Y=1)+P(X=-1, Y=2)=0.2+0.3+0.2=0.7
P(X=1)=P(X=1, Y=0)+P(X=1, Y=1)+P(X=1, Y=2)=0.1+0.1+0.1=0.3
Y的边缘概率分布为
P(Y=0)=P(X=-1, Y=0)+P(X=1, Y=0)=0.2+0.1=0.3
P(Y=1)=P(X=-1, Y=1)+P(X=1, Y=1)=0.3+0.1=0.4
P(Y=2)=P(X=-1, Y=2)+P(X=1, Y=2)=0.2+0.1=0.3
(2) EX=(-1)*P(X=-1)+1*P(X=1)=(-1)*0.7+1*0.3=-0.4
E(X^2)=(-1)^2*P(X=-1)+1^2*P(X=1)=(-1)^2*0.7+1^2*0.3=1
故D(X)=E(X^2)-(EX)^2=1-(-0.4)^2=0.84
D(2X+5)=2^2D(X)=4*0.84=3.36
(3) P(2X+4>0)=P(X>-2)=P(X=-1)+P(X=1)=1