Probability Course
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Date
2025
Authors
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Journal ISSN
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Publisher
Faculty of Sciences
Abstract
I n a world increasingly driven by data and uncertainty, the study of probability has
become a cornerstone of modern science, engineering, finance, and decision-making.
This manuscript is an introduction to probability and is intended for second-year mathematics
students at the University of 20 August 1955, Skikda. It can also be useful for
students from other disciplines seeking to deepen their knowledge of probability.
This first version of the handout is not intended to be a reference work; rather, it is
designed to serve as a memory aid for students approaching a probability course for the
first time.
The content of this manuscript is structured into three chapters:
The first chapter is devoted to the basic notions of probability, defining random experiments
and events, as well as key concepts such as conditional probability, the total probability
formula, Bayes’ theorem, and the notion of independence of events, which is specific
to probability theory.
The second chapter focuses on random variables. After the definition of this notion we
study in detail the two large families of random variables, namely discrete variables and
continuous variables. We provide definitions and key properties of probability mass
function, density function and cumulative distribution functions, including expectation
and variance in both cases. Additionally, we explore inequalities in probability.
Given the importance of probability distribution, the third chapter illustrates the definitions
and main properties of common probability distributions: discrete probability
distributions and continuous probability distributions. We also consider the approximations
between the main distribution such as the convergence of a binomial distribution
to the Poisson distribution, as well the transformations of random variables.
In writing this manuscript, I relied on various recognized references in the field. It is
important to note that this first version does not claim any originality; the content presented
is standard and is found in most books on modern probability theory. Like any
academic work, it may contain errors, and I wish to express my gratitude and thanks in
advance to any colleagues or students who share their feedback and criticisms to assist
in the development of this manuscript