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I want to have a deep understanding of probability.

I've tried William Feller's first book on Probability, and E.T Jaynes' Probability theory - the logic of science (which is very different from most probability books.) But, neither books could hold my interest for long. The first was too boring. The second was too tough to understand.

Please suggest some strategies and books that can help me.

As far as the level of my current knowledge goes, I know basic combinatorial probability, conditional probability, Bayesian probability, binomial, Poisson and Normal distribution. I only know how to apply the normal distribution, not how to derive it.

Saikat
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  • Feller is a classic; you should revisit it later. A very good, entertaining book for beginners is Blitzstein and Hwang, based on Stat 110 at Harvard. – symplectomorphic Jun 15 '16 at 05:50
  • https://books.google.co.in/books/about/Probability_and_Random_Processes.html?id=1rTcR3nIkJcC – Amruth A Jun 15 '16 at 05:51
  • @symplectomorphic What are some strategies I can use not to get bored? – Saikat Jun 15 '16 at 05:53
  • In an introductory level, you're not expected to be able to "derive" the normal distribution. You might consider skipping the first few chapters of the book you get though, since it would just be "review" to you – Em. Jun 15 '16 at 05:53
  • @AmruthA Does your book require knowledge of signals and systems ? Because I don't have that. – Saikat Jun 15 '16 at 05:54
  • @probablyme But, I want to have a deep understanding. – Saikat Jun 15 '16 at 05:55
  • Do you know any topology? Any Real Analysis? Lebesgue Measure? If the answer any of those, especially the latter two, is no, I would suggest learning a bit about them. I can only recommend the one book series I've looked about general abstract measure theory, which are hands down the best analysis books I've ever read for any subject, it's simply called Measure Theory, it's 5 volumes (I have a preference for thorough works, especially when self-studying) by Fremlin (here is a link to the first volume: https://wiki.math.ntnu.no/_media/tma4225/2011/fremlin-mt1.pdf. – Justin Benfield Jun 15 '16 at 05:57
  • @JustinBenfield No, I don't know any real analysis. All the probability I've had so far has not been remotely related to calculus (except Normal distribution). What I mean is, have I reached the limits of what I can understand of probability without learning analysis ? Also, can I directly start with measure theory or do I have to study other books before that ? – Saikat Jun 15 '16 at 06:02
  • A "deep understanding" is very vague. It honestly is not clear what you want. – Em. Jun 15 '16 at 06:03
  • If you want a deep understanding, sooner or later you have to read Jaynes. The "classical statistics" debacle is the greatest disaster in the history of maths and still not over today. – almagest Jun 15 '16 at 06:05
  • @almagest I don't understand what you mean by calling it a disaster. But, Jaynes is really different from other books. It doesn't have many practice problems either. – Saikat Jun 15 '16 at 06:08
  • @user230452: If you truly want a 'deep' understanding, then yes, you do need some analysis, and indeed some measure theory because probability theory rests upon the notion of a probability measure, which is a particular kind of measure space. – Justin Benfield Jun 15 '16 at 06:09
  • @user230452 That is true it is not a textbook. When you say you want a deep understanding of "probability", do you mean of "inference" (which is the general subject - how do we extract useful information from data) or narrowly of probability theory? – almagest Jun 15 '16 at 06:11
  • @JustinBenfield What do you recommend for starting real analysis ? – Saikat Jun 15 '16 at 06:11
  • Actually if u have knowledge in integration then u will understand the normal distribution – SIVA NAGA KUMAR.PERUBOYINA Jun 15 '16 at 06:12
  • @ArmanMalekzade Unfortunately, I don't know how to use chat and it says I don't have enough reputation to talk on there anyway. – Saikat Jun 15 '16 at 06:18
  • @user230452: I haven't taken Real Analysis or read any books on it myself, so I really can't be of help with that question. I can say that I think it's helpful to make sure you feel solid on your calculus (since calculus leads directly to real analysis, where among other things you learn about the lebesgue measure). There is a two volume work on calculus that I've wanted to acquire for some time now because it is rigorous and very thorough (which imo is ideal for self-study because it facilitates answering your own questions). – Justin Benfield Jun 15 '16 at 06:32
  • @user230452: The text I was wanting to acquire is Mathematical Analysis, author: Vladimir A. Zorich – Justin Benfield Jun 15 '16 at 06:58
  • @user230452 not required . – Amruth A Jun 15 '16 at 11:45
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    Does this answer your question? A path to truly understanding probability and statistics –  Dec 31 '20 at 03:49

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