introduction to probability

introduction to probability

$39.95

This book introduces students to probability, statistics, and stochastic processes. It can be used by both students and practitioners in engineering, various sciences, finance, and other related fields. It provides a clear and intuitive approach to these topics while maintaining mathematical accuracy.

The book covers:

  • Basic concepts such as random experiments, probability axioms, conditional probability, and counting methods
  • Single and multiple random variables (discrete, continuous, and mixed), as well as moment-generating functions, characteristic functions, random vectors, and inequalities
  • Limit theorems and convergence
  • Introduction to Bayesian and classical statistics
  • Random processes including processing of random signals, Poisson processes, discrete-time and continuous-time Markov chains, and Brownian motion
  • Simulation using MATLAB, R, and Python (online chapters)

The book contains a large number of solved exercises. The dependency between different sections of this book has been kept to a minimum in order to provide maximum flexibility to instructors and to make the book easy to read for students. Examples of applications—such as engineering, finance, everyday life, etc.—are included to aid in motivating the subject. The digital version of the book, as well as additional materials such as videos, is available at www.probabilitycourse.com

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Description

Introduction to Probability, Statistics, and Random Processes

by Hossein Pishro-Nik (Author)

Introduction to Probability, Statistics, and Random Processes by Hossein Pishro-Nik is a widely used undergraduate-level textbook that introduces probability theory, statistics, and stochastic (random) processes in a single volume. It was published in 2014 by Kappa Research and is approximately 730–750 pages long. (Open Library)

What the book covers

The text progresses from foundational probability to more advanced topics: (Google Books)

  1. Probability fundamentals
    • Sample spaces and events
    • Probability axioms
    • Conditional probability
    • Bayes’ theorem
    • Counting techniques
  2. Random variables
    • Discrete and continuous distributions
    • Expectation and variance
    • Moment-generating functions
    • Joint distributions and random vectors
  3. Limit theorems
    • Laws of large numbers
    • Central limit theorem
    • Convergence concepts
  4. Statistics
    • Estimation
    • Hypothesis testing
    • Bayesian and classical approaches
  5. Random processes
    • Poisson processes
    • Markov chains
    • Brownian motion
    • Random signal processing
  6. Simulation
    • Monte Carlo methods
    • Random number generation
    • Examples using MATLAB and R (with some online materials including Python) (Bookshop.org)

Strengths

  • Clear, intuitive explanations with many worked examples.
  • Covers probability, statistics, and stochastic processes in one coherent text.
  • Includes a large number of solved exercises.
  • Frequently recommended for self-study by students and practitioners. (Bookshop.org)

Mathematical prerequisites

A solid background in:

  • Calculus (especially integration)
  • Basic algebra
  • Some familiarity with mathematical reasoning

Students without calculus can still benefit from the early chapters, but later sections become significantly easier with calculus knowledge. (Reddit)

Who should read it?

This book is a good choice if you are:

  • Studying engineering, computer science, data science, mathematics, economics, or finance.
  • Preparing for machine learning, AI, communications, or stochastic modeling.
  • Looking for a bridge between introductory statistics and more advanced probability theory.

Compared with other popular books

Book Style Level
Introduction to Probability, Statistics, and Random Processes Balanced, applied + theoretical Beginner to intermediate
Introduction to Probability Conceptual, problem-solving focused Intermediate
A First Course in Probability Traditional probability theory Intermediate
All of Statistics Fast-paced statistics overview Intermediate to advanced

If you’re studying probability and statistics for machine learning, data science, or engineering, this is often considered one of the strongest free/self-study resources available. (Reddit)

If you’d like, I can also provide a chapter-by-chapter study plan for this book or explain any chapter in detail.

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