Probability density of function of continuous random variable under non one to one correspondence

To the probability density function(PDF) of the function of continuous random variable,it is required that the range of a random independent variable X with the transfer function y=g(x) has a one to one correspondence.This condition is harsh,and it can not be contented by many transfer functions.In this paper,the formula of the PDF of the function of continuous random variable is developed,in which the above condition is canceled.By this way,more PDF of the functions of continuous random variables can be solved.