The ratio R of two random quantities is frequently encountered in probability and statistics. But while for unidimensional statistical variables the distribution of R can be computed relatively easily ...

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

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: Complex random variables arise naturally in many settings and their properties are of general interest. Past work on complex variables has mainly focused on their second-order structure, as ...

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 ...

For the past several years I’ve been thinking on and off about whether there’s a fruitful category-theoretic perspective on probability theory, or at least a perspective with a category-theoretic ...

Created with R2024a. Compatible with R2024a and later releases. You can use these live scripts as demonstrations in lectures, class activities, or interactive assignments outside class. This module ...