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2. The probability density function (pdf) technique, univariate. Suppose that Y is a continuous random variable with cdf ( ) and domain , and let distribution function. +. + compute sample compute distributional means and variances means and variances. Table I: Corresponding notions between statistics of functions of random variables. 1.1 Distribution Function Technique. Assume that we are given a continuous rrv X with pdf fX. We want to find the pdf of Y = u(X) There are three main methods to find the distribution of a function of one or more random variables. These are to use the CDF, to trans- form the pdf directly or to Method of transformations (inverse mappings). Suppose we know the density function of x. Also suppose that the function y = ?(x) is differentiable and monotonic KEYWORDS: Probabilistic distributions generating method, Distribution classes generating functions, probabilistic distributions classes, probabilistic distribution support. 1. . Access The probability density function (PDF) of a random variable, X, allows you to calculate the probability of an event, as follows: For continuous distributions, theIn summary, we used the distribution function technique to find the p.d.f. of the random function Y = U(X) by: (1) First, finding the cumulative distribution function:. The probability density function (PDF) of a random variable, X, allows you to calculate the probability of an event, as follows: For continuous distributions, theIn summary, we used the distribution function technique to find the p.d.f. of the random function Y = U(X) by: (1) First, finding the cumulative distribution function:.