1, the variance is a function of the random variable X G(X)=∑[X-E(X)]2π, that is, from the definition of variance: D(X)=∑xipi-E(x), the following commonly used calculation formulas can be obtained.

D (x) = ∑ (xipi+e (x) pi-2xipie (x)) = ∑ xipi+∑ e (x) pi-2e (x) = ∑ xipi+e (x)-2e (x) = ∑ xipi-e (x).

2. Let x be a random variable. If E {2} exists, let E {2} be the variance of x, and record it as D(X), Var(X) or DX. That is, d (x) = e {2} is called variance, and σ (x) = d (x) 0.5 (the same dimension as x) is called standard deviation (or mean square deviation). That is, statistics is used to measure the dispersion of a set of data.

Variance describes the dispersion degree between the value of random variable and its mathematical expectation. If the values of x are concentrated, the variance D(X) is small, and if the values of x are scattered, the variance D(X) is large. Therefore, D(X) is a quantity to describe the dispersion degree of X value and a scale to measure the dispersion degree of X value.