概车伦与散理统外「 (2)pw=1的充要条件是，存在常数a,b使 P(Y =a+bX)=1. 事实上，pxx=1→E(Y-(a+X)2]=0 →0=E[(Y-(a+bX)2] =D[Y-(ao+b)+[E(Y-(ao+box)) →D[Y-(a+bX1=0, EY-(a+bX)】=0. 由方差性质知 P{Y-(a+bX)=0}=1,或P{Y=4+bX=1.{ } 1. (2) 1 , , = + = = P Y a bX ρXY 的充要条件是 存在常数 a b 使 事实上, ρXY = 1 2 0 0 0 0 2 0 0 [ ( )] [ ( ( ))] 0 [( ( )) ] D Y a b X E Y a b X E Y a b X = − + + − +  = − + [ ( )] 0,  D Y − a0 + b0X = [ ( )] 0. E Y − a0 + b0X = 由方差性质知 { } 1. 或 P Y = a0 + b0X = [( ( )) ] 0 2  E Y − a0 + b0X = { ( ) 0} 1, P Y − a0 + b0X = =