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 ...

Probability theory forms the mathematical backbone for quantifying uncertainty and random events, providing a rigorous language with which to describe both everyday phenomena and complex scientific ...

Convergence theorems form the backbone of probability theory and statistical inference, ensuring that sequences of random variables behave in a predictable manner as their index grows. These theorems, ...

A courseware module that covers the fundamental concepts in probability theory and their implications in data science. Topics include probability, random variables, and Bayes' Theorem.

ABSTRACT: This methodological article aims to present the type I Pareto distribution in a clear and illustrative manner for better understanding among social researchers. It also provides R scripts ...

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

We start by embedding probability theory into a general theory of measure and integration. This will allow us to derive theorems that may not have been included in the Analysis III course but that are ...

A discrete random variable is a type of random variable that can take on a countable set of distinct values. Common examples include the number of children in a family, the outcome of rolling a die, ...