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[[File:Dice Distribution (bar).svg|thumb|250px|right|
[[File:Dice Distribution (bar).svg|thumb|250px|right|
图1:The [[probability mass function]] (pmf) ''p''(''S'') specifies the probability distribution for the sum ''S'' of counts from two [[dice]]. For example, the figure shows that ''p''(11) = 2/36 = 1/18. The pmf allows the computation of probabilities of events such as ''P''(''S'' > 9) = 1/12 + 1/18 + 1/36 = 1/6, and all other probabilities in the distribution.
图1:The [[probability mass function]] (pmf) ''p''(''S'') specifies the probability distribution for the sum ''S'' of counts from two [[dice]]. For example, the figure shows that ''p''(11) = 2/36 = 1/18. The pmf allows the computation of probabilities of events such as ''P''(''S'' > 9) = 1/12 + 1/18 + 1/36 = 1/6, and all other probabilities in the distribution.
The [[probability mass function (pmf) p(S) specifies the probability distribution for the sum S of counts from two dice. For example, the figure shows that p(11) = 2/36 = 1/18. The pmf allows the computation of probabilities of events such as P(S > 9) = 1/12 + 1/18 + 1/36 = 1/6, and all other probabilities in the distribution.]]
The [[probability mass function (pmf) p(S) specifies the probability distribution for the sum S of counts from two dice. For example, the figure shows that p(11) = 2/36 = 1/18. The pmf allows the computation of probabilities of events such as P(S > 9) = 1/12 + 1/18 + 1/36 = 1/6, and all other probabilities in the distribution.]]
概率质量函数(pmf) p(s)指定两个骰子计数总和s的概率分布。例如，图中显示 p (11) = 2/36 = 1/18。Pmf 允许计算事件的概率，如 p (s > 9) = 1/12 + 1/18 + 1/36 = 1/6，以及分布中的所有其他概率。
--[[用户:普天星相|普天星相]]([[用户讨论:普天星相|讨论]]) 【审校】“概率质量函数(pmf) p(s)指定两个骰子计数总和s的概率分布”一句中“指定”改为“列出了”。
--[[用户:普天星相|普天星相]]([[用户讨论:普天星相|讨论]]) 【审校】“Pmf 允许计算事件的概率”一句中“允许”改为“可用于”。
<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>
--[[用户:普天星相|普天星相]]([[用户讨论:普天星相|讨论]]) 【审校】“6个值中的每一个的概率为1/6”一句中“6个值”改为“1-6这六个值”。
In contrast, when a random variable takes values from a continuum then typically, any individual outcome has probability zero and only events that include infinitely many outcomes, such as intervals, can have positive probability. For example, the probability that a given object weighs ''exactly'' 500 g is zero, because the probability of measuring exactly 500 g tends to zero as the accuracy of our measuring instruments increases. Nevertheless, in quality control one might demand that the probability of a "500 g" package containing between 490 g and 510 g should be no less than 98%, and this demand is less sensitive to the accuracy of measurement instruments.
In contrast, when a random variable takes values from a continuum then typically, any individual outcome has probability zero and only events that include infinitely many outcomes, such as intervals, can have positive probability. For example, the probability that a given object weighs ''exactly'' 500 g is zero, because the probability of measuring exactly 500 g tends to zero as the accuracy of our measuring instruments increases. Nevertheless, in quality control one might demand that the probability of a "500 g" package containing between 490 g and 510 g should be no less than 98%, and this demand is less sensitive to the accuracy of measurement instruments.
相比之下，当一个随机变量从一个连续体中取值时，那么通常情况下，任何单个结果的概率都为零，只有包含无限多个结果的事件，例如间隔，才有正的概率。例如，一个给定的物体重量正好是500克的概率为零，因为随着我们测量仪器精度的提高，正好测量500克的概率趋向于零。然而，在质量控制方面，人们可能会要求包装在490克至510克之间的“500克”包装的可能性不低于98% ，而这一要求对测量仪器的准确性不太敏感。
相比之下，当一个随机变量从一个连续体中取值时，那么通常情况下，任何单个结果的概率都为零，只有包含无限多个结果的事件，例如间隔，才有正的概率。例如，一个给定的物体重量正好是500克的概率为零，因为随着我们测量仪器精度的提高，正好测量500克的概率趋向于零。然而，在质量控制方面，人们可能会要求包装在490克至510克之间的“500克”包装的可能性不低于98% ，而这一要求对测量仪器的准确性不太敏感。
--[[用户:普天星相|普天星相]]([[用户讨论:普天星相|讨论]]) 【审校】“那么通常情况下，任何单个结果的概率都为零，只有包含无限多个结果的事件，例如间隔，才有正的概率”一句改为“通常情况下，任何单个结果的概率都为零，只有包含无限多个结果的事件（例如区间）才有正的概率”。
--[[用户:普天星相|普天星相]]([[用户讨论:普天星相|讨论]]) 【审校】“人们可能会要求包装在490克至510克之间的“500克”包装的可能性不低于98%”一句改为“人们可能会要求介于490克至510克之间的“500克”包装出现的概率不低于98%”。
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 [[Integration (mathematics)|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 [[Integration (mathematics)|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.