Distribution Functions of random variables in February 22

The distribution function of random variables is not easy to understand. I found the following online:

Definition 2.1.2It is a random variable, an arbitrary real number, a function

Is called the distribution function.
Distributed functions have the following properties:
(1 ).
(2) monotonous, that is, if.
(3) right continuity refers to the existence of the right limit at any place and equal to, that is, the right limit.
On the contrary, functions with the above three properties must be the distribution function of a random variable.
(4 ).
(1) What are the functions of introducing random variable distribution functions?
For random variables, we need to know not only what values are taken, but also the probability of getting these values. In addition, we need to know not only the probability of getting a value, more importantly, you need to know the probability of a value in any finite range, and

Therefore, the distribution function fully describes the statistical regularity of random variables.
On the other hand, a distributed function is a common real-value function that we are already familiar with in advanced mathematics. It has a very good nature, with the random variables and distributed functions, it is like setting up a bridge between the random phenomenon and higher education, so that we can use the method of higher education to study the statistical law of the random phenomenon.
(2)Are the sum of the two distribution functions still the distribution function?
No. In fact, if we set it to two distributed functions
.

F (x) indicates a number, which is a frequency value (between 0 and 1) and a frequency of x <X.