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. \[\int_{-\infty}^{\infty}f\left(x\right)dx=1\] ...

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 ...

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.

In the early development of probability theory, only discrete random variables (although not called random variables at the time) were considered. Isaac Newton (1643-1727) considered the idea of ...

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 ...

Abstract: The law of large numbers in probability theory states that the average of random variables converges to its expected value in some sense under some conditions. Sometimes, random factors and ...

(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 ...

Will Kenton is an expert on the economy and investing laws and regulations. He previously held senior editorial roles at Investopedia and Kapitall Wire and holds a MA in Economics from The New School ...

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 ...