D(X) refers to variance, and E(X) refers to expectation. E(X) says that the simple point is the average value, and the specific method is to sum and then divide by the quantity.

d(x)=e[x-e(x)]^2=e{x^2-2xe(x)+[e(x)]^2}=e(x^2)-2[e(x)]^2+[e(x)]^2。

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 many practical problems, it is of great significance to study variance or deviation.

Extended data

Properties of variance

1, let c be a constant, then D(C)=0 (constant has no fluctuation);

2.D(cx)=C2D(x) (constant square extraction);

Certificate:

D(-X)=D(X), D(-2X)=4D(X) (variance is not negative).

When x and y are independent of each other, the third term is zero.