An introduction to probability theory and its applications

Name: An introduction to probability theory and its applications
ISBN: 0471257087

by William Feller · first published 1950

11mentions

8recommended by

9HN commenters

2008–2024first – last mentioned

89% recommend11% neutral

Why HN recommends it

Classic two-volume probability text praised as deep yet readable. Volume 1 is a staple of undergraduate math courses, while Volume 2 suits graduate-level study. It still reads well decades after the 1960s.

Summarised by Claude from recommending comments

Data & Statistics

Vol. 2 has series: Wiley series in probability and mathematical statistics. Bibliographical footnotes. "Some books on cagnate subjects": v. 2, p. 615-616.

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What Hacker News says

Myrmornis · Mar 6, 2014 · Recommends

Well it's too late to get any points for this inference now, but I'm going to claim that there was a strong clue that the author of the PDF was old: the bitcoin paper cites "An Introduction to Probability Theory and Its Applications" by William Feller. This is a classic, from the 1960s, but I don't think it's very well known among people under 40 (correct me if I'm wrong).
on “The Face Behind Bitcoin?” ↗
kurtosis · May 28, 2008 · Recommends

The all time classic at the level your looking for is William Feller's two volume set "Introduction to probability theory and its applications"- if you can find a copy. A good university library should have a copy. On wikipedia, it claims that Persi Diaconis (of the seven shuffles theorem fame) was motivated to finish high school after dropping…
on “Ask YC: Best book to learns statistics?” ↗
lajosbacs · Nov 24, 2022 · Recommends

An Introduction to Probability Theory and its Applications By William Feller, written in 1968 but feels very fresh even today.
on “Ask HN: Math books you recommend just for the way they are written?” ↗
antegamisou · Jun 16, 2023 · Recommends

…Elementary Probability Theory: With Stochastic Processes and an Introduction to Mathematical Finance by K. L. Chung & F. AitSahlia https://www.amazon.com/Elementary-Probability-Theory-Introdu... An Introduction to Probability Theory and Its Applications Vol. 1 by W. Feller https://www.amazon.com/Introduction-Probability-Theory-Appli... I'm sure there are some great video lectures on the subject as well, but unfortunately I can't point you to any relevant…
on “Probability and Markets by Jane Street [pdf]” ↗
mamonster · Mar 28, 2024 · Recommends

William Feller: An introduction to Probability Theory and Its Applications Volumes 1 and 2 - Volume 1 is considered the "classic" in most math undergrad courses, Volume 2 is for masters level students. Billingsley Probability and Measure - For more advanced probability you…
on “Ask HN: List of best probability books from beginner to advance?” ↗
sanand · Jun 19, 2009 · Recommends

…Concrete Mathematics. Hoffman and Kunze, Linear Algebra (there are several free online books on Linear Algebra and Vector Spaces, Strang, Axler, Lang Halmos and Shilov are also recommended). Feller, An Introduction to Probability Theory and Its Applications. If you're not studying for exams and you have plenty of time on your hands, try the following algorithm: 1. Dive into some random chapter in the book and attempt the first exercise in that chapter. 2.…
on “Ask HN: good math books” ↗
waldrews · Oct 25, 2009 · Recommends

…quick-road-to-hacking-power agenda): For classical deep stats theory, everyone I know begins with Cassela and Berger's Statistical Inference. Don't expect algorithms in this though. On the probability side: Feller's An Introduction to Probability Theory and Its Applications. Deep, readable, sometimes funny, full of "whoa" insights. Would be hard to actually grok every chapter in both volumes, but you read it for insight into the power of probability and then use it as…
on “Ask HN: Statistics for hackers?” ↗
francasso · Mar 11, 2018 · Recommends

…Niven, Zuckerman, Montgomery Some more advanced stuff - Algebra: Algebra - Artin or Algebra, Chapter 0 - Aluffi - Complex Analysis: Functions of One Complex Variable I - Conway - Probability Basics: An Introduction to Probability Theory and its Applications I - Feller - Real Analysis and functional analysis basics: Real Analysis - Folland - Basic Differential Geometry: Elementary Differential Geometry - O'Neill - Riemann Surfaces (algebraic take): Algebraic…
on “Ask HN: How to self-learn math?” ↗
graycat · Jan 30, 2020 · Mentions

…variables. Often in practice can check these assumptions well enough just intuitively. Then as in Çinlar can quickly derive lots of nice, useful results. (2)The Renewal Theorem. As in William Feller, 'An Introduction to Probability Theory and Its Applications, Second Edition, Volume II', ISBN 0-471-25709-5, roughly, with meager assumptions and approximately, if the arrivals are from many different independent sources, not necessarily Poisson, then the resulting…
on “Some Useful Probability Facts for Systems Programming” ↗
graycat · Apr 19, 2020 · Mentions

…arrival times have exponential distribution and why we get a Poisson process, Çinlar has a nice simple, intuitive, useful axiomatic derivation. There is more via the renewal theorem in William Feller, An Introduction to Probability Theory and Its Applications, Second Edition, Volume II, ISBN 0-471-25709-5, John Wiley & Sons, New York, 1971.
on “Forecasting s-curves is hard” ↗
graycat · Aug 3, 2019 · Mentions

…and many more, we have the true statement Event A Could Trigger the Next Global Financial Crisis Yup. But there is a nice result in stochastic processes, the renewal theorem, in William Feller, An Introduction to Probability Theory and Its Applications, Second Edition, Volume II, ISBN 0-471-25709-5, John Wiley & Sons, New York, 1971. that shows that the events that "Could Trigger the Next Global Financial Crisis" arrive as a Poisson arrival process…
on “Climate Change Could Trigger the Next Global Financial Crisis” ↗