设X-某随机变量； P(x) - 随机变量的概率密度；
e(X)-随机变量的期望；d(x)-随机变量的方差.
设x表示n重贝努里实验中事件a出现的次数,且p（a）=p.
a不出现, q=1-p,
P(x)=p^x (1-p)^(1-x)
d(x)=e(x^2)-[e(x)]^2
e(x)=sum(x=0,1)x[p^x] (1-p)^(1-x)=(0)(1-p)+(1)p=p
e(x^2)=sum(x=0,1)[(x-p)^2] p^x *(1-p)^(1-x)
=p^2(1-p)+(1-p)^2 p=p(1-p)
d(x)=e(x^2)-[e(x)]^2=p(1-p)-p^2=p(1-2p)