随机变量(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)落入圆x2+y2=r22(r﹤R)内的概率．
(1)∫+∞-∞∫+∞-∞f(x,y)dxdy =A∫∫x2+y2≤R2[R-√(x2+y2)]dxdy =A∫∫p≤R(R-p)pdpdθ =A∫2π0dθ∫R0(Rp-p2)dp =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-p)pdpdθ =3/πR3∫2π0dθ∫x0(Rp-p2)dp=(3r2/R2)(1-2r/3R)
