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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，指定一个概率质量函数 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>

Continuous probability distributions can be described in several ways. The probability density function describes the infinitesimal probability of any given value, and the probability that the outcome lies in a given interval can be computed by integrating the probability density function over that interval. The probability that the possible values lie in some fixed interval can be related to the way sums converge to an integral; therefore, continuous probability is based on the definition of an integral.  

Continuous probability distributions can be described in several ways. The probability density function describes the infinitesimal probability of any given value, and the probability that the outcome lies in a given interval can be computed by integrating the probability density function over that interval. The probability that the possible values lie in some fixed interval can be related to the way sums converge to an integral; therefore, continuous probability is based on the definition of an integral.  

[[File:Combined Cumulative Distribution Graphs.png|thumb|455x455px|

[[File:Combined Cumulative Distribution Graphs.png|thumb|455x455px|