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 ...

In a raffle with 20 tickets, 6 tickets are drawn for prizes. The first prize winner gets $\$20$, 2 second prize winners get $\$10$, and three third prize winners get $\$5$. What is the sample space ...

College of Mathematics and Physics, Shijiazhuang University of Economics, Shijiazhuang, China. Science College, Beijing University of Civil Engineering and Architecture, Beijing, China. [1] W. Liu, ...

The accurate characterization of input processes for simulation models can require the representation of dependencies among input values. Results are presented on the generation of dependent ...

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 ...

In order to simulate many real-world problems, after fitting a probability distribution to a sequence of numbers, there is a need to artificially generate variables (called pseudo-random variables) ...

Abstract: This paper proposes using collisions of Pareto random variables in traffic analysis and in generating fictitious network traffic that follows various Pareto distributions. Pareto ...