D(X/3+Y/2)怎么算?
如果X,Y相互獨(dú)立,那么
D(X/3 + Y/2) = D(X)/9 + D(Y)/4；
否則要用到X,Y的協(xié)方差：
令：Z=X/3+Y/2
D(Z)=D(X/3+Y/2)=E[(X-EX)²/9 + (Y-EY)²/4 + 2(X-EX)(Y-EY)/(2*3)]
= E[(X-EX)²/9] + E[(Y-EY)²/4] + E[(X-EX)(Y-EY)/3]
= D(X)/9 + D(Y)/4 + COV(X,Y)/3
其中：COV(X,Y) = E[(X-EX)(Y-EY)] 為X,Y的協(xié)方差.
如果x,y獨(dú)立,那么cov（x,y）＝0.