如题所述
第1个回答 2020-01-31
证明：E(ax+b)=aE(x)+b
D(x)=E(x^2)-(E(x))^2
D(ax+b)=E((ax+b)^2)-(E(x))^2
=E(a^2x^2+2abx+b^2)-(E(ax+b))^2
=a^2*E(x^2)+2ab*E(x)+b^2-(aE(x)+b)^2
=a^2*E(x^2)+2ab*E(x)+b^2-(a^2(E(x))^2+2abE(x)+b^2)
=a^2*E(x^2)-a^2(E(x))^2=a^2(E(x^2)-(E(x)^2)
=a^2*D(x)
证毕!
D(x)=E(x^2)-(E(x))^2
D(ax+b)=E((ax+b)^2)-(E(x))^2
=E(a^2x^2+2abx+b^2)-(E(ax+b))^2
=a^2*E(x^2)+2ab*E(x)+b^2-(aE(x)+b)^2
=a^2*E(x^2)+2ab*E(x)+b^2-(a^2(E(x))^2+2abE(x)+b^2)
=a^2*E(x^2)-a^2(E(x))^2=a^2(E(x^2)-(E(x)^2)
=a^2*D(x)
证毕!
