Roll a die and ask students to identify the random variable. Since a die can only take on values of 1, 2, 3, 4, 5, or 6, this is a discrete random variable. Repeat ...

The total area under the curve must equal 1, representing the fact that the probability of some outcome occurring within the entire range is certain. \[\int_{-\infty}^{\infty}f\left(x\right)dx=1\] ...

A courseware module that covers the fundamental concepts in probability theory and their implications in data science. Topics include probability, random variables, and Bayes' Theorem.

Abstract: A random variable is a measurable function from an uncertainty space to the set of real numbers, which is used to model randomness. An uncertain variable is a measurable function from ...

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 ...

This paper considers a classical linear simultaneous equations model with random coefficients on the endogenous variables. Simultaneous equations models are used to study social interactions, ...

(1) PROF. FRECHET'S "Généralités" represents the first volume only of a treatise which, as a whole, is to form part of the very important "Traité du calcul des probabilités"edited by Prof. Borel. The ...

Injuries limit the athletes' ability to participate fully in their training and competitive process. They are detrimental to performance, affecting the athletes psychologically while limiting ...