设随机变量(X,Y)的分布律为
\u8bbe\u968f\u673a\u53d8\u91cfX\u7684\u5206\u5e03\u5f8b\u4e3aX -2 -1 0 1 2\uff0c\u6c42Y=X^2\u7684\u5206\u5e03\u5f8b\uff0cY\u7684\u5206\u5e03\u51fd\u6570\uff0cP{Y<=1}\u8bbe\u968f\u673a\u53d8\u91cfX\u7684\u5206\u5e03\u5f8b\u4e3a
X -2 -1 0 1 2
P 1/5 1/6 1/5 1/15 11/30
\u4e8e\u662f\uff0cY=X^2\u7684\u5206\u5e03\u5f8b\u4e3a
X^2 0 1 4
P 1/5 7/30 17/30
Y\u7684\u5206\u5e03\u51fd\u6570\u4e3a
F(y) = P{Y<=y}
\u5373
F(y) = 0\uff0c y<0\uff0c
= 1/5\uff0c 0<=y<1\uff0c
= 13/30\uff0c1<=y<4\uff0c
= 1\uff0c y>4\uff0c
\u800c
P{Y<=1} = F(1) = 13/30\u3002
\u7531\u4e8e:P(X=0, Y=0)=P(X=1, Y=0)=P(X=0, Y=1)=P(X=1, Y=1)= 1/4.
P(Z=1)= P(X=1, Y=0)+ P(X=0, Y=1)+ P(X=1, Y=1)= 3/4.
P(Z=0) =:P(X=0, Y=0) =1/4..
Z\u7684\u5206\u5e03\u5f8b: P(Z=0)=1/4, P(Z=1) = 3/4.
P{1《X《2，3《Y《4}= P（X=1，Y=3）+P（X=1，Y=4）+P（X=2，Y=3）+P（X=2，Y=4）=1/16+1/4=5/16
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