连续型随机变量函数分布密度的一种简单求法

A Simple Solution of Distribution Density of Continuous Random Variable Function

求随机变量函数的分布是概率论中的一个重要课题,无论是在理论还是在应用上都有着十分重要的意义.对于连续型随机变量ξ来说,可由分布函数的定义先求出随机变量ξ和它的函数η=f(ξ)这个新的随机变量的分布函数之间的联系,然后通过求导,得到密度函数之间的联系,从而求得η的分布密度.该方法严谨直观,计算简单、实用性强.

Solving the distribution of random variable function which is of great significance whether in theory or in application is an important question in probability theory. As for continuous random variable, the connection of distribution function between random variable and its function - - a new random variable can be obtained first according to the definition of distribution function, then the connection between distribution densities can be obtained by derivation; thus the distribution density is solved.