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How to calculate the mathematical expectation value of several single data?
This is very simple. The mathematical expectation of several data refers to the average value of these data.

The definition of mathematical expectation is this. Expected value of mathematics

English (x)

=

X 1*p(X 1)

+

X2*p(X2)

+

……

+

Xn*p(Xn)

X 1, x2, x3, ..., xn are these data, and p (x 1), p (x2), p (x3), ... p (xn) are probability functions of passing data. In random data transmission, p (x 1), p (x2), p (x3), ... p (xn) are understood as the frequency of data f(Xi )+ 0, x2, x3, ..., xn. Then:

English (x)

=

X 1*p(X 1)

+

X2*p(X2)

+

……

+

Xn*p(Xn)

=

X 1*f 1(X 1)

+

X2*f2(X2)

+

……

+

Xn*fn(Xn)

It is easy to prove that E(X) is the arithmetic mean of these data.

Let's give an example, for example, there are several numbers:

1, 1,2,5,2,6,5,8,9,4,8, 1

1 appears three times, accounting for 3/ 12 of all data occurrences, and this 3/ 12 is the frequency corresponding to 1. Similarly, f(2) can be calculated.

=

2/ 12 f(5)

=

2/ 12

,

Female (6)

=

1/ 12

,

Eighth groups

=

2/ 12

,

Female (9)

=

1/ 12

,

Female (4)

=

1/ 12

According to the definition of mathematical expectation:

English (x)

=

2*f(2)

+

5*f(5)

+

6*f(6)

+

8*f(8)

+

9*f(9)

+

4*f(4)

=

13/3

therefore

English (x)

=

13/3,

Now calculate the arithmetic average of these numbers:

Auxiliary amplifier (abbreviation for auxiliary amplifier)

=

( 1+ 1+2+5+2+6+5+8+9+4+8+ 1)/ 12

=

13/3

So E(X)

=

Auxiliary amplifier (abbreviation for auxiliary amplifier)

=

13/3