=E{X^2-2XE(X)+[E(X)]^2}

=E(X^2)-2[E(X)]^2+[E(X)]^2

The mathematical expectation is that x is a random variable. If E {[x-e (x)] 2} exists, then E {[x-e (x)] 2} is called the variance of x, and is recorded as D(X), Var(X) or DX. That is, d (x) = e {[x-e (x)] 2} is called variance, and σ (x) = d (x) 0.5 (the same dimension as x) is called standard deviation (or variance).

Extended data:

For fixed n and p, when k increases, the probability P{X=k} first increases until it reaches the maximum value, and then monotonically decreases. It can be proved that the general binomial distribution also has this property, and:

When (n+ 1)p is not an integer, the binomial probability P{X=k} reaches the maximum when k=[(n+ 1)p];

When (n+ 1)p is an integer, the binomial probability P{X=k} reaches the maximum when k=(n+ 1)p and k=(n+ 1)p- 1. ?

Baidu Encyclopedia-Binomial Distribution