更改

To define probability distributions for the simplest cases, it is necessary to distinguish between discrete and continuous random variables. In the discrete case, it is sufficient to specify a probability mass function p assigning a probability to each possible outcome: for example, when throwing a fair die, each of the six values 1 to 6 has the probability 1/6. The probability of an event is then defined to be the sum of the probabilities of the outcomes that satisfy the event; for example, the probability of the event "the dice rolls an even value" is  

To define probability distributions for the simplest cases, it is necessary to distinguish between discrete and continuous random variables. In the discrete case, it is sufficient to specify a probability mass function p assigning a probability to each possible outcome: for example, when throwing a fair die, each of the six values 1 to 6 has the probability 1/6. The probability of an event is then defined to be the sum of the probabilities of the outcomes that satisfy the event; for example, the probability of the event "the dice rolls an even value" is  

为了定义最简单的概率分布，有必要区分离散和连续的随机变量。在离散情况下，指定一个'''<font color="#ff8000">概率质量函数 Probability Mass Function</font>'''p 就足够了，它为每个可能的结果赋予一个概率: 例如，当投掷一个骰子时，6个值中的每一个的概率为1/6。然后将事件的概率定义为满足事件的结果的概率之和; 例如，事件”骰子掷出偶数值”的概率是

为了定义最简单的概率分布，有必要区分离散和连续的随机变量。在离散情况下，指定一个'''<font color="#ff8000">概率质量函数 Probability Mass Function</font>''' P就足够了，它为每个可能的结果赋予一个概率: 例如，当投掷一个骰子时，6个值中的每一个的概率为1/6。然后将事件的概率定义为满足事件的结果的概率之和; 例如，事件”骰子掷出偶数值”的概率是

<math>p(2) + p(4) + p(6) = 1/6+1/6+1/6=1/2.</math>

<math>p(2) + p(4) + p(6) = 1/6+1/6+1/6=1/2.</math>

* [[Categorical distribution]], for a single categorical outcome (e.g. yes/no/maybe in a survey); a generalization of the [[Bernoulli distribution]]

* [[Categorical distribution]], for a single categorical outcome (e.g. yes/no/maybe in a survey); a generalization of the [[Bernoulli distribution]]

针对单个分类结果的分类分布（例如，调查中的是/否/也许）；伯努利分布的一般化

针对单个分类结果的'''<font color="#ff8000">分类分布 Categorical Distribution</font>'''（例如，调查中的是/否/也许）；伯努利分布的一般化

* [[Multinomial distribution]], for the number of each type of categorical outcome, given a fixed number of total outcomes; a generalization of the [[binomial distribution]]

* [[Multinomial distribution]], for the number of each type of categorical outcome, given a fixed number of total outcomes; a generalization of the [[binomial distribution]]

* [[Multivariate hypergeometric distribution]], similar to the [[multinomial distribution]], but using [[sampling without replacement]]; a generalization of the [[hypergeometric distribution]]

* [[Multivariate hypergeometric distribution]], similar to the [[multinomial distribution]], but using [[sampling without replacement]]; a generalization of the [[hypergeometric distribution]]

=== Poisson process (events that occur independently with a given rate) 泊松过程（以给定速率独立发生的事件）===

=== Poisson process (events that occur independently with a given rate) 泊松过程（以给定速率独立发生的事件）===