What is Reddit's opinion of Probability and Random Processes?

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Do you know some basic real analysis? If so, I'd probably recommend something like Grimmett and Stirzaker. I don't have any recommendations for a lower-level course, unfortunately.

God, this forum has turned into just probability after probability. Also, this question was asked last week.

My first choice is Ross, as it is the gold standard for undergrad probability classes, but others a good too I suppose. I agree that Probability and Random Processes is good too.

I had to take a course that had probability and mathematical statistic courses as prerequisites so I read 'Probability and Random Processes' to catch up. I thought it was an awesome book.

Link to Amazon

I mean the honors version of the undergraduate course, Honors Theory of Probability. The texts used are either [Grimmet and Stirzaker](https://www.amazon.com/Probability-Random-Processes-Geoffrey-Grimmett/dp/0198572220) or [Knowing the odds](https://www.amazon.com/Knowing-Odds-Introduction-Probability-Mathematics/dp/0821885324) .

https://www.amazon.com/Probability-Random-Processes-Geoffrey-Grimmett/dp/0198572220

Okay,

For probability, there are three books I recommend for learning. The first is the text by Grimmett and Stirzaker. This is a real probability text which will take you as far as the basics of Eto calculus. It's not measure-theoretic, but it does a very good job explaining the concepts and bridging the intuition with the formalism. If you were to buy only one text, this is the one I would recommend for the average person.

The second text is the one by Williams. This is the most slick probability book I know. It will get you to the central limit theorem and martingales faster than any other text, and it's great on intuition. The problems in the back of the book are excellent and difficult. I pull this one down occasionally to refresh my memory. This one is measure-theoretic.

The last text is the one by Durrett. This one is beefy and difficult. But once you already have a solid baseline, this book will take you far. This book has become my canonical reference. I learned mostly from this book, and I appreciate its volume of material and problems. The low amazon star average indicates that many people have trouble with it. However, we used it at Michigan, and it was a good course. This book assumes that you are fluent in measure theory.

For statistics, I literally don't know any good textbooks. Wasserman's All of Statistics is okay, at best. But it doesn't go into enough depth in any of its topics. The canonical introductory book is Casella and Berger, which no one loves. It has all the basics, but it's expensive and horrendously boring.

My favorite introductory book is the slim book by Silvey. Try to get a cheap copy on amazon.

Frankly, I don't think introductory statistics is very interesting, and so just cobble together some basic understanding via a cheap book and YouTube videos. Then move onto the fun stuff.

Probability and Random Processes by Grimmett is a good introduction to probability.

Mathematical Statistics by Wackerly is a comprehensive introduction to basic statistics.

Probability and Statistical Inference by Nitis goes into the statistical theory from heavier probability background.

The first two are fairly basic and the last is more involved but probably contains very few applied techniques.

My preference in probability theory book is always this: http://www.amazon.com/Probability-Random-Processes-Geoffrey-Grimmett/dp/0198572220 . It is exceptionally well written.