离散型随机变量(discrete variable)

• 定义：由分离的、不可分割的范畴组成，在邻近范畴之间没有值存在的变量。
• 举例：
  1. 计数数字：掷骰子得到的1和2之间没有其他值存在；
  2. 不同类别：人格障碍分类；
  3. 时间、长度、质量……

• Definition: A variable consisting of separate, indivisible categories in which no value exists between neighboring categories.
• Example:
  1. Counting digits: No other value exists between the 1 and the 2 you get when you roll a die;
  2. Different classifications: Classification of personality disorders；
  3. Time, length, mass…

连续型随机变量(continuous variable)

• 定义：在任意两个观测值之间都存在无限多个可能值，可以分割成无限多个组成部分的变量。
• 表示方式：一般可以用一条连续的实数直线表示，在实数直线上存在无数个点，在任意两个相邻点之间依然可以找到无数个点。
• 精确界限：在说到一个连续型变量的某个观测值时，往往指实数直线上的一个区间，构成这个区间的边界被称为精确界限。例如，23代表的区间是从22.5到23.5，22.5是精确下限，23.5是精确上限。

• Definition: A variable in which there are infinite possible values between any two observations and which can be divided into infinite components.
• Expression: Generally it is represented by a continuous straight line of real numbers, on which there are infinite points and you can find an infinite number of points between any two adjacant points.
• Real limit: When speaking of an observation of a continuous variable, it often refers to an interval on the real line, and the boundary forming this interval is called the real limit. For instance, 23 represents the range from 22.5 to 23.5, where 22.5 is the lower real limit and 23.5 is the upper real limit.

连续型变量与离散型变量的关系(the relationship between continuous variables and discrete variables)

• 当离散型变量取值空间较大，取值点比较密集时，也可以视为连续型变量。将连续型变量分组，可以作为离散型变量处理。
• When the value space of a discrete variable is large and the value points are dense, it can also be regarded as a continuous variable. Grouping continuous variables can be treated as discrete variables.