This book will be particularly useful to those interested in learning how probability theory can be applied to the study of phenomena in fields such as engineering, computer science, management science, the physical and social sciences, and operations research. Ideally, this text would be used in a one-year course in probability models, or a one-semester course in introductory probability theory or a course in elementary stochastic processes.
If anybody asks for a recommendation for an introductory probability book, then my suggestion would be the book by Henk Tijms, Understanding Probability, second edition, Cambridge University Press, 2007. This book first explains the basic ideas and concepts of probability through the use of motivating real-world examples before presenting the theory in a very clear way. I found a nice feature of the book the fact that simulation is deliberately used to develop probabilistic intuition. The book also discusses more advanced topics you will not easily find in other introductory probability books. The more advanced topics include Kelly betting, random walks, and Brownian motion, Benford's law, and absorbing Markov chains for success runs. Another asset of the book is a great introduction to Bayesian inference.
Introduction To Probability Models 10th Pdf 11
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While not a book, Sal Khan's site: offers dozens of short videos that provide introductions to probability and statistics. Many of the videos even have problem sets associated with them. Khan provides accessible and often intuitive explanations.
A bit surprised that neither of these have been mentioned. Grinstead & Snell's Introduction to Probability is a good comprehensive introduction, and after that Feller's Introduction to Probability Theory and its applications is a very good serious treatment after introductory probability.
Build foundational knowledge of data science with this introduction to probabilistic models, including random processes and the basic elements of statistical inference -- Part of the MITx MicroMasters program in Statistics and Data Science.
The videos in Part I introduce the general framework of probability models, multiple discrete or continuous random variables, expectations, conditional distributions, and various powerful tools of general applicability.
Thus instead of building probability distributions from scratch, we will rely on a simplification called a parametric probability model. A parametric probability model is a probability distribution that can be completely described using a relatively small set of numbers, far smaller than the number of distinct outcomes in the sample space. These numbers are called the parameters of the distribution. There are lots of commonly used parametric models that have been invented for specific purposes. A large part of getting better at probability modeling is to learn about these existing parametric models, and to gain an appreciation for the typical kinds of real-world problems where each one is appropriate.
One of the simplest parametric models in all of probability theory is called the binomial distribution, which generalizes the idea of flipping a coin many times and counting the number of heads that come up. The binomial distribution is a useful parametric model for any situation with the following properties:
Below are given an overview over the status so far and the plans for the future lectures.
All references are to chapter and sections in the textbook (Ross: Introduction to Probability models, 10th edition).
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