1, different values E(X)=E(X), e (x 2) = d (x)+e (x) * e (x).

2. The meaning is different. E(X) represents the expectation of x, and e (x 2) represents the expectation of x 2.

3. The solution is different. The solution of E(X 2) is x 2 times the density function for integration, and the solution of e (x) is x times the probability density for integration.

Extended data:

The essence of expectation:

Let c be a constant and x and y be two random variables. The following are the important properties of mathematical expectations:

1、E(C)=C .

2、E(CX)=CE(X).

3、E(X+Y)=E(X)+E(Y).

4. when x and y are independent of each other, E(XY)=E(X)*E(Y).

Property 3 and property 4 can be extended to the sum or product of any finite number of independent random variables.

From the essence of mathematical expectation:

When the data distribution is scattered (that is, the data fluctuates greatly around the average value), the sum of squares of differences between each data and the average value is large, and the variance is large; When the data distribution is concentrated, the sum of squares of the differences between each data and the average value is very small. Therefore, the greater the variance, the greater the data fluctuation; The smaller the variance, the smaller the data fluctuation.

Baidu Encyclopedia-Mathematical Expectation

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