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→Continuous probability distribution 连续概率分布
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--[[用户:普天星相|普天星相]]([[用户讨论:普天星相|讨论]]) 【审校】以上性质没有翻译。第一行应为“<math>F(x)</math>是非减的”；第三行"and"改为“和”；第四行"and"改为“以及”；第五行应为“由于黎曼积分的性质，<math>F(x)</math>连续”
It is also possible to think in the opposite direction, which allows more flexibility. Say <math>F(x)</math> is a function that satisfies all but the last of the properties above, then <math>F</math> represents the cumulative density function for some random variable: a discrete random variable if <math>F</math> is a step function, and a continuous random variable otherwise.<ref>See Theorem 2.1 of {{harvp|Vapnik|1998}}, or [[Lebesgue's decomposition theorem]]. The section [[#Delta-function_representation]] may also be of interest.</ref> This allows for continuous distributions that has a cumulative density function, but not a probability density function, such as the [[Cantor distribution]].
It is also possible to think in the opposite direction, which allows more flexibility. Say <math>F(x)</math> is a function that satisfies all but the last of the properties above, then <math>F</math> represents the cumulative density function for some random variable: a discrete random variable if <math>F</math> is a step function, and a continuous random variable otherwise.<ref>See Theorem 2.1 of {{harvp|Vapnik|1998}}, or [[Lebesgue's decomposition theorem]]. The section [[#Delta-function_representation]] may also be of interest.</ref> This allows for continuous distributions that has a cumulative density function, but not a probability density function, such as the [[Cantor distribution]].