The probability density function (pdf) of any given continuous random variable is defined as f(p) = the probability value of any given sample/point within the sample space - interpreted as the relative likelihood of the sample/point.
In order to define a valid pdf, you need the probability function and the sample space of your random variable. Note that the integral of the pdf over the whole sample space should always equal 1 for a valid pdf.
If you are interested in numerical methods, I can suggest you the Monte Carlo simulation. use the MC simulation to generate the responses and then find the desired PDF using the generated outputs.