Probability theory is like the crystal ball of mathematics, helping us predict the likelihood of events occurring. The magic number always lies between 0 and 1, inclusive, where 0 means “impossible” ...

Abstract: In this chapter, we introduce the concept of a random variable and develop the procedures for characterizing random variables, including the cumulative distribution function, as well as the ...

This chapter reviews uniform and Gaussian random variables (RVs). It describes the empirical probability density function (PDF) of RVs and provides its comparison with the theoretical PDF. Using ...

This note suggests that expressing a distribution function as a mixture of suitably chosen distribution functions leads to improved methods for generating random variables in a computer. The idea is ...

A simple procedure for deriving the probability density function (pdf) for sums of uniformly distributed random variables is offered. This method is suited to introductory courses in probability and ...