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A '''continuous probability distribution''' is a probability distribution whose support is an uncountable set, such as an interval in the real line.<ref>{{Cite book|title=Introduction to probability models|author1=Sheldon M. Ross|date=2010|publisher=Elsevier}}</ref> They are uniquely characterized by a [[cumulative density function]]{{dn|date=August 2020}} that can be used to calculate the probability for each subset of the support. There are many examples of continuous probability distributions: [[normal distribution|normal]], [[Uniform distribution (continuous)|uniform]], [[Chi-squared distribution|chi-squared]], and [[List of probability distributions#Continuous distributions|others]].

A '''continuous probability distribution''' is a probability distribution whose support is an uncountable set, such as an interval in the real line.<ref>{{Cite book|title=Introduction to probability models|author1=Sheldon M. Ross|date=2010|publisher=Elsevier}}</ref> They are uniquely characterized by a [[cumulative density function]]{{dn|date=August 2020}} that can be used to calculate the probability for each subset of the support. There are many examples of continuous probability distributions: [[normal distribution|normal]], [[Uniform distribution (continuous)|uniform]], [[Chi-squared distribution|chi-squared]], and [[List of probability distributions#Continuous distributions|others]].

连续概率分布是一种概率分布，其支持是不可计数的集合，例如实线中的间隔。它们的独特之处在于可用于计算支撑的每个子集的概率的累积密度函数[需要消除歧义]。连续概率分布有很多示例：正态分布，均匀分布，卡方分布和其他分布。

连续概率分布是一种概率分布，其支持是不可计数的集合，例如实线中的间隔。它们的独特之处在于可用于计算支撑的每个子集的概率的累积密度函数[需要消除歧义]。连续概率分布有很多示例：正态分布，均匀分布，卡方分布和其他分布。

A random variable <math>X</math> has a continuous probability distribution if there is a function <math>f: \mathbb{R} \rightarrow [0, \infty)</math> such that for each interval <math>I \subset \mathbb{R}</math> the probability of <math>X</math> belonging to <math>I</math> is given by the integral of <math>f</math> over <math>I</math>.<ref>Chapter 3.2 of {{harvp|DeGroot, Morris H.|Schervish, Mark J.|2002}}</ref> For example, if <math>I = [a, b]</math> then we would have:

A random variable <math>X</math> has a continuous probability distribution if there is a function <math>f: \mathbb{R} \rightarrow [0, \infty)</math> such that for each interval <math>I \subset \mathbb{R}</math> the probability of <math>X</math> belonging to <math>I</math> is given by the integral of <math>f</math> over <math>I</math>.<ref>Chapter 3.2 of {{harvp|DeGroot, Morris H.|Schervish, Mark J.|2002}}</ref> For example, if <math>I = [a, b]</math> then we would have: