连续型随机变量的概率密度与分布函数

在概率论与数理统计中,根据连续型随机变量的定义,讨论连续型随机变量的概率密度与分布函数的互求问题。结合实例分析给出结论:(1)对于一维连续型随机变量,当分布函数的非连续导数点是有限个时,只要将概率密度补充适当的定义,即可满足要求。(2)对于二维连续型随机变量,当分布函数的二阶混合偏导数在有限条光滑曲线上不连续时,只要将概率密度补充适当的定义,即可满足要求。

In probability theory and mathematical statistics,according to the definition of continuous random variables,the mutual problem of probability density and distribution function of continuous random variables is discussed.Combined with the example analysis,the conclusion is given:(1)For one-dimensional continuous random variables,when the non-continuous derivative points of the distribution function are finite,the probability density can be supplemented with appropriate definitions to meet the requirements.(2)For two-dimensional continuous random variables,when the second-order mixed partial derivatives of the distribution function are discontinuous on the finite strip smooth curve,the probability density can be supplemented with appropriate definitions to meet the requirements.