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: 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 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 ...

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 ...

Abstract: Laplace transform is a very import conclusion guided by complex function integral, which occupies a very important position in applied mathematics. Especially when solving the initial value ...