Probability Book For Beginner.

Question

I am a graduate school freshman.

I did not take a probability lecture.

So I don't have anything about Probability.

Could you suggest Probability book No matter What book level?

Answer 1

This is a standard and good introduction to probability: https://www.amazon.co.uk/Probability-Introduction-Oxford-Science-Publications/dp/0198532644

I would also recommend avoiding the approach recommended by Justin in the comments. He is right that measure theory is important in advanced probability theory, however, going straight to this without having first studied introductory level probability I believe would be confusing, unhelpful and just not necessary. Furthermore measure theory itself is a topic which first requires a good foundation in dealing with abstract maths and so not a good place to start.

Answer 2

This is a surprisingly difficult question to answer. My natural instinct as a mathematician at heart (though no PhD, yet) is to echo Justin and tell you to go straight into measure theory and then worry about probability. Classical probability theory is indeed best understood in a measure theoretic context, though it's historical development tells a different story. On one hand, even if you get a probability book for "beginners", you'll be learning the axioms of measure theory (or at least some of them) without knowing it, so you might as well dive straight into the deep end. On the other hand, if you don't have a sufficient background, you risk losing interest due to the lack of context and motivation. Really, it all depends on your goals and background and if you could elaborate on those, I'd be more capable of pointing you in the right direction.

If you do indeed want to dive into the deep end, Ash and Doleans-Dade's Measure and Probability Theory is your best bet IMO. It has a nice balance of exposition and rigor but if you've never taken at least a calculus class (the very minimum pre-req IMO) you'll be completely lost.

Edit: Now that I read your question more closely, I see you say graduate school "freshman" (I've never heard that characterization of a grad student but I assume 1st year) so it really depends on your field of study. If it is mathematics or statistics, you absolutely need the measure theoretic version.

Answer 3

I think the book Probability Theory by Heinz Bauer is a very good text on probability theory. It contains an extensive discussion of all the basic parts of the theory and is very readable. The book requires, however, a modest background in measure theory.

The original version of the book from 1973, Probability Theory and Elements of Measure Theory, contains all the necessary background in measure theory. Later versions of the book are split into two books, the parts on measure and probability theory are published as Measure and Integration Theory and Probability Theory, respectively.

Answer 4

@EHH I completely agree for Grimmett ! A very valuable book also by Grimmett and a coauthor (Stirzacker): (http://www.oupcanada.com/catalog/9780198572220.html). It has a somewhat larger scope (including stochastic processes). A very good point: a huge amount of exercices with an invaluable book of solutions.

Answer 5

Art of Problem Solving's Intermediate Counting and Probability is a book for students with solid basics. If you would like something easier, Introduction to Counting and Probability(also by AoPS) is perfect for beginners, no matter what age. AoPS textbooks are written by the nation's best mathmeticians and contains thourough explanations, well written problems, and a complete solution manual.