ab是两个相互独立的随机变量.则D(a+b)=Da+Db我觉得D(a+b)=(a+b-Ea-Eb)^2XpDa+Db=(a-Ea)^2Xp+(b-Eb)^2Xp
问题描述:
ab是两个相互独立的随机变量.则D(a+b)=Da+Db
我觉得
D(a+b)=(a+b-Ea-Eb)^2Xp
Da+Db=(a-Ea)^2Xp+(b-Eb)^2Xp
答
D(a+b)=E[(a+b-Ea-Eb)^2]=E[(a-Ea)^2+(a-Ea)*(b-Eb)*2+(b-Eb)^2]=E(a-Ea)^2+E(b-Eb)^2+E(a-Ea)*(b-Eb)*2=Da+Db+E(a-Ea)*(b-Eb)*2;
因为ab是两个相互独立的随机变量,所以E(a-Ea)*(b-Eb)*2=2*E(a-Ea)*E(b-Eb)=2*(Ea-Ea)*(Eb-Eb)=0;所以D(a+b)=Da+Db