Equation d (x) = e {[x-E(X)] 2} = e (x 2)-[e (x)] 2, where e (x) stands for mathematical expectation.

For continuous random variable X, if its definition domain is (a, b) and the probability density function is f(x), the formula for calculating the variance of continuous random variable X is d (x) = (x-μ) 2 f (x) dx.

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

Extended data:

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

D(CX )=C2D(X) (constant square extraction, C is constant, X is random variable);

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

If x and y are independent of each other, then the evidence is recorded.

The first two items are just D(X) and D(Y), and the third item is expanded as follows.

When x and y are independent of each other,

So the third term is zero.

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