高三的书上题 关于离散型随机变量的期望和方差.我想知道D(a§+b)=a^2D§ 这个方差的性质是如何推导的?请就使用高

1,设b为常数,也可将它看成随机变量求期望和方差．
E(b) = b,b - E(b) = 0,D(b) = E((b - E(b))^2) = 0．
2.设a为常数,
E(a§)= a E(§),
D(a§) = E((a§ - E(a§))^2)
= E((a§ - a E(§))^2)
= E(a^2 *(§ - E(§))^2)
= a^2 * E((§ - E(§))^2)
= a^2 * D(§)
3.E(a§ + b) = E(a§) + E(b) = a E(§) + b,
D(a§ + b) = E(((a§ + b) - E((a§ + b)))^2)
= E(((a§ + b) - (a E(§) + b))^2)
= E(a^2 * (§- E(§)^2 )
= a^2 * E((§- E(§))^2)
= a^2 * D(§)．
－－－－－－－－－－－－－－
从头到尾,只用到两个公式
E(aX) = a E(X),E(X + Y) = E(X) + E(Y),
以及方差的定义
D(X) = E((X - E(X))^2)
这些应该是高中学过的吧?