问题
问答题
设随机变量X的概率密度函数为
对X进行两次独立观察,其结果分别记为
答案
参考答案:如下图,
当(y1,y2)∈D0,即y1<0或y2<0时,F(y1,y2)=0;
当(y1,y2)∈D,即0≤y1<1,0≤y2<1时,
[*]
F(y1,y2)=P{Y1≤Y1,Y2≤Y2}
=P{Y1=0,Y2=0}=P11;
当(Y1,Y2)∈D1,即0≤y1<1,y2≥1时,
F(y1,y2)=P{Y1≤y1,Y2≤y2}
=P{Y1=0,Y2=0}+P{Y1=0,Y2=1}
=P11+P12;
当(y1,y2)∈D2,即y1≥1,0≤y2<1时,
F(y1,y2)=P{Y1=0,Y2=0}+P{Y1=1,Y2=0}=P11+P21;
当(y1,y2)∈D3,即y1≥1,y2≥1时,
F(y1,y2)=P{Y1≤y1,Y2≤Y2}
=P{Y1≤1,Y2≤1