Continuous Random Variables

The basic theory of the probability has been discussed in Chap. 1. That knowledge based on the set theory is essential to understand the notion of probability. However, it lacks applicability in many cases. For instance, let consider that very large number of events is under investigation. Calculations of probabilities of any arbitrary outcomes would require a great deal of effort. For this reason, the general concept of the probability theory is developed by means of random variables and corresponding probability functions, namely the probability distribution function and the probability density function. In general, a function maps elements of a well-defined set to another well-defined set. Let \(x \in A \) and \(y \in B\), a function f(x) defines the transformation from set A to set B, and it is denoted as; $$\begin{aligned} f : x \rightarrow y \end{aligned}$$ A random variable, X, is a function related with the outcomes of a certain random experiment.