联合概率密度函数设随机向量（X,Y）的分布函数为F(x,y)=A(B+arctan x/2)(C+arctan y/3)

F(-∞,y)=A*(B-π/2)(C+arctan y/3)=0,B=π/2
F(x,-∞)=A*(B+arctan x/2)(C-π/2)=0,C=π/2
F(+∞,+∞)=A(B+π/2)(C+π/2)=1,A=1/π²
答：A=1/π²,B=C=π/2
f(x,y)=δ²F(x,y)/δxδy=[2/(x²+4)][3/(y²+9)]/π²=6/(x²+4)(y²+9)π²
答：联合密度函数为6/(x²+4)(y²+9)π²