Ch4-63 例4已知X,Y相互独立,且都服从 N(0,0.5),求E(|X-Y|) 解X~N(.0.5,y~N(0,0.5) E(X-Y)=0,D(X-)=1 故X-Y~N(0,1) E(X-YD=z z 2丌 2c+ ze 2 d 2兀Ch4-63 例4 已知X ,Y 相互独立, 且都服从 N (0,0.5), 求 E( | X – Y | ). 解 X ~ N(0,0.5),Y ~ N(0,0.5) E(X −Y) = 0,D(X −Y) =1 故 X −Y ~ N(0,1) E X Y z e dz z 2 2 2 1 (| |) | | + − − − =    2 2 2 2 0 2 = = + −  ze dz z