例1.设(x,Y)的分布函数为 F(x, y)=A(B+arctan (C+arctan 求常数ABC的值及概率P(X≤3y≤4} 解由分布函数的性质 =F(3,4 16 F(+,+∞)=1,F(-∞,+∞)=0,F(+,-∞)=0 A(B+)(C+)=1 A A(B-C+)=0一B A(B+(C-1=0 xπ-2π-2 2F( , ) 1, + + = F( , ) 0 , − + = F(+ ,−) = 0 (X ,Y) ) 4 )( arctan 3 ( , ) ( arctan y C x F x y = A B + + P X Y { 3, 4}.   例1. 设 的分布函数为 求常数 A B C , , 的值及概率 解 由分布函数的性质 得 ) 1 2 )( 2 ( + + =   A B C ) 0 2 )( 2 ( − + =   A B C ) 0 2 )( 2 ( + − =   A B C 2 1  A = 2  B = 2  C = = F(3, 4) 16 9 =