From the definition of variance, the following commonly used calculation formulas can be obtained:
D(X)=E(X^2)-[E(X)]^2
S 2 = [(x 1-x pull) 2+(x2-x pull) 2+(x3-x pull) 2+…+(xn-x pull) 2]/n
Several important properties of variance (assuming that each variance exists).
(1) Let c be a constant, then D(c)=0.
(2) If X is a random variable and C is a constant, then D (CX) = (C 2) D (X).
(3) Let x and y be two independent random variables, then D(X+Y)=D(X)+D(Y).
(4) The necessary and sufficient condition for d (x) = 0 is that x takes the constant value c with the probability of 1, that is, P{X=c}= 1, where e (x) = c.