Variance is a measure of dispersion when probability theory and statistical variance measure random variables or a set of data. Variance in probability theory is used to measure the deviation between random variables and their mathematical expectations (that is, the mean value).

In probability theory and mathematical statistics, mathematical expectation (or mean for short, or expectation) is one of the most basic mathematical characteristics, which is the sum of the results multiplied by the probability of each possible result in an experiment. It reflects the average value of random variables.

The formula for calculating the correlation between variance and expected value is as follows:

dx=e(x-e(x))^2=e{x^2-2xe(x)+(e(x))^2}=e(x^2)2(e(x))^2+(e(x))^2

Extended data:

For continuous random variable X, if the definition domain is (a, b) and the probability density function is F(X), the variance calculation formula of continuous random variable X is: d (x) = (x-) 2f (x) dx. The square seal difference describes the degree of dispersion between the value of a random variable and its mathematical expectation. (The greater the standard deviation and variance, the greater the dispersion)

If the value of x is concentrated, the variance of D(X) is small; If the value of x is dispersed, then the variance of D(X) is very large.

So D(X) is a measure of X's dispersion, and it is a measure of X's dispersion.

References:

Baidu Encyclopedia-Mathematical Expectation

References:

Baidu encyclopedia-variance