Expected difference (expected) ar; Ance) is also called expected variance and variance obtained through numerous measurements. The expected value of variance l) (2) is equal to the variance of the population.

The nature of mathematical expectation variance;

1, let x be a random variable and c be a constant, then E(CX)=CE(X).

2. If x and y are any two random variables, then E(X+Y)=E(X)+E(Y).

3. Let x and y be independent random variables, then E(XY)=E(X)E(Y).

4. let c be a constant, then e (c) = c

When probability theory and statistical variance measure random variables or a set of data, expected variance is a measure of deviation.

Variance in probability theory is used to measure the deviation between random variables and their mathematical expectations (that is, the mean value). The variance (sample variance) in statistics is the average value of the square of the difference between each sample value and the average value of all sample values.

In statistical description, expected variance is used to calculate the difference between each variable (observed value) and the population mean. In order to avoid the phenomenon that the average sum deviation is zero and the average square sum deviation is affected by the sample size, the average deviation of the average square sum is used to describe the variation degree of variables.

Variance describes the deviation between random variables and mathematical expectations. A single deviation is the average of the square deviation, that is, the variance without the influence of symbols, which is recorded as E(X): the direct calculation formula separates the discrete type from the continuous type.

A calculation formula is also derived: "variance is equal to the average of the sum of squares of deviations of each data and its arithmetic average". Among them, they are discrete and continuous calculation formulas respectively. It is called standard deviation or mean square deviation, and variance describes the degree of fluctuation.