Abstract: In this chapter, we first introduce the joint statistical behavior of multiple random variables, and then the focus turns toward the marginal and conditional cdfs, pdfs, and pmfs. In the ...

This note suggests that expressing a distribution function as a mixture of suitably chosen distribution functions leads to improved methods for generating random variables in a computer. The idea is ...

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 ...

Explain why probability is important to statistics and data science. See the relationship between conditional and independent events in a statistical experiment. Calculate the expectation and variance ...

{% file src="../.gitbook/assets/chapter-04-1-kor.pdf" caption="Chapter 4-1 (Korean)" %} {% file src="../.gitbook/assets/chapter-04-2-kor.pdf" caption="Chapter 4-2 ...

The Hong Kong University of Science and Technology course "Python and Statistics for Financial Analysis" by Prof. Xuhu Wan on Coursera (Feb. 2023). Week 1 - Visualizing and Munging Stock Data Why do ...

Let P = (pjk) be the transition matrix of an ergodic, finite Markov chain with no cyclically moving sub-classes. For each possible transition (j, k), let Hjk(x) be a distribution function admitting a ...