Prob/Stats Looking for a probability and statistics textbook

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The discussion centers on finding a suitable textbook for self-studying probability and statistics, particularly for someone with a strong background in calculus and elementary ordinary differential equations. The recommended textbook from MIT OpenCourseWare is deemed comprehensive but potentially too advanced for AP Statistics, as it covers university-level probability theory and statistics. Participants question the necessity of studying AP Statistics given the user's mathematical background and suggest that it may be overly simplistic.Suggestions include exploring other textbooks, such as Degroot and Schervish, which could provide a more rigorous foundation, though they note it typically requires two semesters to cover thoroughly. The conversation also highlights the importance of applying knowledge through practical projects, such as card counting or machine learning, to enhance understanding and engagement with the material. Additionally, resources like the freely available "The Practice of Statistics" by Blitzstein and Hwang are recommended as valuable study aids. Overall, the emphasis is on finding a balance between rigorous mathematical understanding and practical application in the study of probability and statistics.
Falgun
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I want to learn some probability & statistics on my own. I am well versed in Calc 1-3 , elementary ODEs and very little linear algebra. I want a comprehensive , introductory textbook which is NOT COOKBOOK STYLE. I might be self studying AP statistics next term so if the book covers everything I need for the AP, that would be really convenient. Although I am not studying just for the exam so I want to pick a book which will be useful later too.

When I browsed MIT OCW, I found the recommended textbook to be :
https://www.amazon.com/dp/0134995473/?tag=pfamazon01-20

Can anyone who has used the book tell me if it meets my needs?

Thanks in advance.
 
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Falgun said:
I want to learn some probability & statistics on my own. I am well versed in Calc 1-3 , elementary ODEs and very little linear algebra. I want a comprehensive , introductory textbook which is NOT COOKBOOK STYLE. I might be self studying AP statistics next term so if the book covers everything I need for the AP, that would be really convenient. Although I am not studying just for the exam so I want to pick a book which will be useful later too.

When I browsed MIT OCW, I found the recommended textbook to be :
https://www.amazon.com/dp/0134995473/?tag=pfamazon01-20

Can anyone who has used the book tell me if it meets my needs?

Thanks in advance.
Its decent. I used it for a class. It would be overkill for ap statistics. The book you linked is actually a probability theory / with stats books at the university level.

So my question is. If you already know Cal 1-3 and ODE. Why learn ap stats?

There is always going to be a bit of hand waiving in Statistics, unless you have at least graduate level mathematics understanding.

For probability theory, I really enjoyed this book https://www.amazon.com/dp/1138369918/?tag=pfamazon01-20
 
MidgetDwarf said:
Its decent. I used it for a class. It would be overkill for ap statistics. The book you linked is actually a probability theory / with stats books at the university level.

So my question is. If you already know Cal 1-3 and ODE. Why learn ap stats?

There is always going to be a bit of hand waiving in Statistics, unless you have at least graduate level mathematics understanding.

For probability theory, I really enjoyed this book https://www.amazon.com/dp/1138369918/?tag=pfamazon01-2
First of all thank you for your reply.

To answer your question , I'm a physics guy who likes pure mathematics. I will definitely need some prob/stats . Also it never hurts to get a AP under my belt. My options right now are to learn out of a "MATH METHODS" book like Arfken or Riley Hobson Bence or get a standard AP textbook. I know a pure math book would need some measure theory and what not.

I am looking for a middle road. Would you say that AP stats is a subset of Degroot/schervish? Also can I reasonably complete my self study in the course of 4-5 months?

If the answer to these questions is a NO then please recommend another book.
 
Falgun said:
First of all thank you for your reply.

To answer your question , I'm a physics guy who likes pure mathematics. I will definitely need some prob/stats . Also it never hurts to get a AP under my belt. My options right now are to learn out of a "MATH METHODS" book like Arfken or Riley Hobson Bence or get a standard AP textbook. I know a pure math book would need some measure theory and what not.

I am looking for a middle road. Would you say that AP stats is a subset of Degroot/schervish? Also can I reasonably complete my self study in the course of 4-5 months?

If the answer to these questions is a NO then please recommend another book.
I never took AP stats, or bothered to learn what is in it. From my understanding, and having helped my gf when she took it 5 years ago (she graduate in psychology). It was extremely trivial in the sense that I think its possible with a person with at least a precalculus understanding of mathematics could do well in the course.
It appeared to me, when I glanced, that it is mostly plug and chug, and understanding definition/formulas (when they are valid) to pass the course.

So yes, Degroot would cover it.

Its hard to say how long it would take you to read the book. By read, I mean do the majority of exercises without looking at solutions, and digesting/understanding the information in the text.

Typically, Degroot is a 2 semester textbook. So maybe 3 months to get through the probability section, and 3 months to get through stats portion. But that is hard to say, since I do not know if you are familiar reading mathematical text, at what level, and how other personal/work commitments you may have.

Probability is a bit weird, and some people click naturally with it and others dont.

If you are learning for fun. Then check out the book in the link I posted in my initial response. It is superior to the probability portion of Degroot. (I own the first edition of that book)...
 
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If you are self-studying, I would highly recommend picking a project that will involve the knowledge of the subject you are trying to study instead of slogging through a textbook. First, reading a textbook straight up is boring, and second you want to apply that knowledge to some application anyway.

In the case of probability, what about looking into blackjack and learning card counting, that will teach you the basics of discrete probability where you can reference all sorts of textbooks. If you are looking for continuous applications, try implementing your machine learning system or analyzing physical experiments.

I personally think that's the more fun approach. The material across textbooks are largely the same.
 
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MidgetDwarf said:
For probability theory, I really enjoyed this book https://www.amazon.com/dp/1138369918/?tag=pfamazon01-20
I browsed through the table of contents and it is indeed impressive. As a plus it seems to have been written in an informal but not handwavy way. But does the book require any previous knowledge of R ?
 
Falgun said:
I browsed through the table of contents and it is indeed impressive. As a plus it seems to have been written in an informal but not handwavy way. But does the book require any previous knowledge of R ?
No R needed. Yes, it is a bit informal. But it teaches you to think in a probabilistic way. Exercises are more interesting then Degroot. It also covers more interesting problems, and presents the material in a more motivated/interesting manner.

Like I mentioned before, to move away from an informal approach, one needs measure theory or higher. So any book at this level will be informal.
 
MidgetDwarf said:
No R needed. Yes, it is a bit informal. But it teaches you to think in a probabilistic way. Exercises are more interesting then Degroot. It also covers more interesting problems, and presents the material in a more motivated/interesting manner.

Like I mentioned before, to move away from an informal approach, one needs measure theory or higher. So any book at this level will be informal.
Thanks a lot!
 
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