Substitute into the formula. Unified score on [a, b].

Expectation:

EX=∫{ from -a product to a} xf(x) dx.

= ∫ {From -a product to a} x/2a dx.

= x 2/4a | {upper A, lower a}.

=0。

E (x 2) = ∫ {from -a product to a} (x 2) * f (x) dx.

= ∫ {From -a product to A} x 2/2ad x.

= x3/6a | {Up A, Down -a}.

=(a^2)/3。

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

It should be noted that the expected value is not necessarily equal to the common sense "expectation"-"expected value" is not necessarily equal to every result. The expected value is the average of the output values of variables. The expected value is not necessarily contained in the set of output values of variables.

The law of large numbers stipulates that as the number of repetitions approaches infinity, the arithmetic average of numerical values almost inevitably converges to the expected value.

Summarized as follows:

Both discrete random variables and continuous random variables are determined by the range of random variables.

Variables can only take discrete natural numbers, that is, discrete random variables. For example, if you toss 20 coins at a time, K coins face up, and K is a random variable. The value of k can only be natural number 0, 1, 2, …, 20, but not decimal number 3.5 or irrational number, so k is a discrete random variable.