2.40 设二维随机变量(X,Y)的联合分布函数为
来源:学生作业帮 编辑:灵鹊做题网作业帮 分类:数学作业 时间:2024/04/29 05:35:28
2.40 设二维随机变量(X,Y)的联合分布函数为
F(x,y)=A(B+arctan x/2)(C+arctan Y/3)
求:(1)系数A,B及C;(2)(X,Y)的联合概率密度;(3)边缘分布函数及边缘概率密度.随机变量X与y是否独立?
F(x,y)=A(B+arctan x/2)(C+arctan Y/3)
求:(1)系数A,B及C;(2)(X,Y)的联合概率密度;(3)边缘分布函数及边缘概率密度.随机变量X与y是否独立?
由性质得:
F(+∞,+∞)=1,
则
A(B+arctan x/2)(C+arctan Y/3) =A(B+π/2)(C+π/3)
F(-∞,+∞)=0
A(B+arctan x/2)(C+arctan Y/3) =A(B-π/2)(C+π/3)
F(+∞,-∞)=0
A(B+arctan x/2)(C+arctan Y/3) =A(B+π/2)(C-π/2)
解得:A=6/(11π),B=π/2,C=π/2
(X,Y)的联合概率密度:
6/(11π)(π/2+arctan x/2)(π/2+arctan Y/3)
边缘分布函数及边缘概率密度:
f(x)=∫f(x,y)dy
f(y)=∫f(x,y)dx
f(x,y)=d^2(F(x,y))/dxdy
所以f(x)=d(F(x,y))/dx=6/(11π)*2/(x^2+4)*(π/2+arctan Y/3)
f(y)=d(F(x,y))/dy=6/(11π)*(π/2+arctan x/2)*3/(x^2+9)
F(+∞,+∞)=1,
则
A(B+arctan x/2)(C+arctan Y/3) =A(B+π/2)(C+π/3)
F(-∞,+∞)=0
A(B+arctan x/2)(C+arctan Y/3) =A(B-π/2)(C+π/3)
F(+∞,-∞)=0
A(B+arctan x/2)(C+arctan Y/3) =A(B+π/2)(C-π/2)
解得:A=6/(11π),B=π/2,C=π/2
(X,Y)的联合概率密度:
6/(11π)(π/2+arctan x/2)(π/2+arctan Y/3)
边缘分布函数及边缘概率密度:
f(x)=∫f(x,y)dy
f(y)=∫f(x,y)dx
f(x,y)=d^2(F(x,y))/dxdy
所以f(x)=d(F(x,y))/dx=6/(11π)*2/(x^2+4)*(π/2+arctan Y/3)
f(y)=d(F(x,y))/dy=6/(11π)*(π/2+arctan x/2)*3/(x^2+9)
2.40 设二维随机变量(X,Y)的联合分布函数为
设二维随机变量(X,Y)的联合分布律为:
概率论设二维随机变量(x,y)的联合密度函数
设二维随机变量(X,Y)的联合概率密度函数
设二维随机变量(x,y)的联合分布函数为 F(x,y)=a(b+arctan(x/2))(c+arctan(y/3))
设二维随机变量(X,Y)的联合密度函数为
概率与统计:设二维随机变量(X,Y)的联合密度函数为,如图
设二维随机变量(X,Y)的联合密度函数为.求概率等.
概率论与数理统计题3设二维连续型随机变量(X,Y)的联合分布函数为F(x,y)=A(B+arctanx/2)(C+arc
设二维连续型随机变量(X,Y)的联合分布函数为F(x,y)=A(B+arctanx/2)(C+arctany/3),判断
设二维随机变量(X,Y)的联合分布函数为F(X,Y)=A(B+arctanX)(C+arcY).求
设二维连续型随机变量(X,Y)的联合分布函数为F(x,y)=A(B+arctanx/2)(C+arctany/3)求AB