2数学期望的性质: (1)E(c)=c (2)E(aX)=aE(X); E(X+Y=EX+EY (4)若X与Y是独立的,则E(XY=EXEY 证明:(2) 离散型X aX ax, ax,... ax Pp p2 n E(ax)=ax p+ax2 p2+.+axn pn+=aE(X) 连续型X-fx(x,Y=ax,则,Y 不妨设a>0, EYc+∞ + yfr(ydy y-x()dy=al ∫x()d(=) +0 z =a 3x(z)dz=aEX2.数学期望的性质: (1)E(c)=c; (2)E(aX)=aE(X); (3)E(X+Y)=EX+EY (4) 若X与Y是独立的,则E(XY)=EXEY 证明:(2) 离散型 X x1 x2 ... xn ... P p1 p2 ... pn ... aX ax1 ax2 ... axn ... P p1 p2 ... pn ... 则 E(aX)= ax1 p1+ax2 p2+ ...+axn pn+...=aE(X) 连续型:X~fX(x),Y=aX,则,Y~ ( ) | | 1 a y f a X ,不妨设a>0, EY = =  +  − yf y dy Y ( )  + − dy a y f a y X ( ) 1  + − = ( ) ( ) a y d a y f a y a X  +  − = a zf z dz X 令 ( ) =aEX z a y =