I have just been learning probability density function (pdf) and there is something I need to ask. I understand the idea that for any value v, the pdf (f(v)) gives the probability that a value picked from a data set is less than v. It seems ok to find mean,variance, skewness etc. when f(v) is known. However, how is the expression for f(v) arrived at. If you have a data set given, can the pdf be found numerically? Thank you.