- A random variable is a variable whose value is unknown or a function that assigns values to each of an experiment's outcomes. - A random variable can be either "discrete" (having specific values) or ...

Discrete and continuous random variables are two types of numerical quantities that can vary unpredictably due to chance or uncertainty. They are widely used in probability and statistics to model ...

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 ...

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 ...

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 ...

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 ...