12.设二维随机变量(X,Y服从二维正态分布: f(x,y)tAb e 求(X,落在椭圆+y=k2内的概率 解:P(X)∈R!= z(R:",+,≤K2) 2元DR 2丌 de abre 2 dr=1-e tAb x=arcose,y=brine19 12. 设二维随机变量(X,Y)服从二维正态分布: 求:(X,Y)落在椭圆 内的概率. 解:          2 2 2 2 1 2 2 2 2 2 2 1 [( ) ] = ( ) 2 x y - a b R x y P X,Y R e dxdy R : κ ab a b    .     2 2 2 2 2 0 0 1 = 1 2 r k k - d abre dr = - e ab   令 x = arcosθ, y = brsin