随机向量(X，Y)的概率密度
f(x，y)=
{A(R-√x2+y2)，x2+y2≤R2；
{0，其他．
求：(1)系数A；
(2)(X，Y)落人圆x2+y2=r2(r＜R)内的概率．
【正确答案】：(1)∫+∞-∞∫+∞-∞(x，y)dxdy =A∫∫x2+y2≤R2(R-√x2+y2)dxdy =A∫∫ρ≤R(R-ρ)ρdρdθ=A∫2π0dθ∫R0(Rρ-ρ2)dρ =A(πR3/3)=1， 故A=3/πR3． (2)设D为圆域x2+y2＜r2，则 P((X，Y)∈D)=∫∫3/πR3(R-ρ)ρdρdθ =3/πR3∫2π0dθ(Rρ-ρ2)dρ=3r2/R2(1-2r/3R)．
