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