Probability is the backbone of data science and machine learning, providing essential tools to model uncertainty and variability. This article explores the foundational concepts: random variables, ...

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 ...

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: This book introduces the basic concepts of set theory, measure theory, the axiomatic theory of probability, random variables and multidimensional random variables, functions of random ...

Learn how probability distributions help investors assess potential returns and manage risks on assets like stocks. Discover ...

ABSTRACT: This paper derives a mathematical description of the complex stretch processor’s response to bandlimited Gaussian noise having arbitrary center frequency and bandwidth. The description 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 ...

Ivan Bajic (ibajic at ensc.sfu.ca) Office hours: Monday and Wednesday, 13:00-14:00 online (Zoom, see the link in course materials) Introduction to the theories of probability and random variables, and ...

The joint probability of two or more variables being “extreme” is relevant in Flood and Coastal Risk Management (FCRM) in various contexts, including: Assessing the likelihood of extreme peak flow ...