A set of formulas about expectation, variance, point estimation and so on in high school mathematics are urgently sought. There is also a comparison between two people, which is better, the variance is bigger or smaller. Let x be a random variable, and if e {[x-e (x)] 2} exists, then e {[x-e (x)] 2} is the variance of x, which is recorded as D(X) or DX. That is, d (x) = e {[x-e (x)] 2}, σ (x) = d (x) 0.5 (the same dimension as x) is called standard deviation or mean square deviation.

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.