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 ...

A discrete random variable is a type of random variable that can take on a countable set of distinct values. Common examples include the number of children in a family, the outcome of rolling a die, ...

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 ...

The main property of a discrete joint probability distribution can be stated as the sum of all non-zero probabilities is 1. The next line shows this as a formula. The marginal distribution of X can be ...