3)随机变量函数的数学期望 定理31.1设X是随机变量,Y=g(X),且E(g(X)在,则 (1)若X为离散型PX=x)pn=1,2,,则E(g(X)=∑9(x) (2)若X为连续型随机变量X-(x.则E(9(X∥=[(x)(x 定理31.2设g(XY)为随机变量XY的函数E[g(X,Y)]存在, (1)若(X,Y)为离散型随机向量P(X=x,Y=y)=pij=12 则E/8X,Y=∑∑9(x,y,)P (2)若(X,Y)为连续型随机向量、X,Y)fxy),则 elg(X,)/ ∫∫ g(x, y)f(x, y)dxdy 返回返回 定理3.1.1 设X是随机变量,Y=g(X),且E(g(X))存在,则; (1)若X为离散型,P(X=xn )=pn ,n=1,2,...,则 = n n pn E(g(X )) g(x ) (2)若X为连续型随机变量,X~f(x),则  + − E( g( X )) = g( x )f ( x )dx =  i j i j pi j E[ g( X ,Y )] g( x , y ) 定理3.1.2 设g(X,Y)为随机变量X,Y的函数,E[g(X,Y)]存在, (1)若(X,Y)为离散型随机向量,P(X=xi ,Y=yj )=pij ,(i,j=1,2…), 则 (2)若(X,Y)为连续型随机向量,(X,Y)~f(x,y),则   + − + − E[ g( X ,Y )] = g( x, y )f ( x, y )dxdy (3) 随机变量函数的数学期望