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Are there any good books that explain important concepts of probability theory like probability distribution functions and cumulative distribution functions?

Please, avoid referring books like "Mathematical Statistics and Data Analysis" by John Rice which start with simple permutation concepts and then, suddenly (in 2nd chapter) take a leap assuming knowledge in real-analysis, multiple and surface integrals and begin describing CDFs and PDFs and illustrating them in 3-dimensional figures. One is left scratching head as to how everything is connected.

I am looking for self-study books and any book in the same category as "Calculus for the Practical Man" would be of great help.

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    $\begingroup$ What level of sophistication are you looking for? You mention Rice and Calculus for the Practical Man. You also mention "very simple" permutation concepts, so you must be comfortable with some math. When you say statistical theory, what do you mean? The examples you mention are more in the vein of elementary probability theory. $\endgroup$ – cardinal Sep 17 '11 at 13:27
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    $\begingroup$ My point of asking is that you can learn a good amount of elementary probability theory with only a decent grasp of calculus. You can learn a decent amount of (classical) applied statistics without calculus as long as you are willing to accept many formulas without a tremendous amount of motivation. It's, unfortunately, pretty difficult to get too deep into statistical theory (as I understand that term) without the elementary probability theory and a greater familiarity with calculus. $\endgroup$ – cardinal Sep 17 '11 at 13:29
  • $\begingroup$ Thanks Cardinal. I understand that I cannot go much far in statistical theory without good knowledge in Calculus and I am not looking for a non-mathematical text here. The problem I find with Rice's book is that it takes a sudden leap and I am left wondering what should I have known or know to understand this material. On the other hand "Practical Man" slowly builds concepts from elementary blocks and occasionally reiterates them. The latter series has made visible to me the relationships in Mathematics and I am left me wondering why I feared Calculus for so long. $\endgroup$ – VKs Sep 18 '11 at 3:05
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    $\begingroup$ Thanks for that response. If you are looking for something like Rice's text, but "better", my personal favorite is Mood, Graybill, and Boes, Introduction to the theory of statistics, 3rd ed., 1974. It has long been out of print and so can be expensive to get a hold of. It's also a bit more advanced book, even then some of it's more modern competitors like Casella & Berger. At any rate, I find the writing very clear; it moves at the right pace, generally, and has great examples and exercises. Using an elementary probability book like Ross's would probably be good as a supplement. $\endgroup$ – cardinal Sep 18 '11 at 11:55
  • $\begingroup$ If you are also interested in online lectures try coursera.org/course/probability or more "mathy": youtube.com/watch?v=KbB0FjPg0mw $\endgroup$ – Tim Oct 29 '15 at 11:02
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I recommend Head First Statistics. The 'Head First' Series is of superior didactic quality and fun to read. It has a lot of exercises, and was one of the few books were I liked doing the exercises. http://www.amazon.com/Head-First-Statistics-Dawn-Griffiths/dp/0596527586

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    $\begingroup$ Any book in this series causes so much distraction that for me it is no-go, no matter if it is math, programming or playing guitar. But, OP MMV. $\endgroup$ – greenoldman Sep 21 '11 at 10:47
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I was looking for the same a week ago. I found from another post on stackexchange about this book Intuitive biostatistics: A Nonmathematical Guide to Statistical Thinking by Harvey Motulsky. I think the second part of the title is pretty lame. But generally I have/had no problems in understanding the math, but found none of them explaining concepts clear enough for me. I just ordered this book based on the reviews, so I can't give an opinion about it myself yet. There were good reviews on amazon and on stackexchange (although many preferred the 1st edition to 2nd). If you're looking for something totally different, this might interest you.

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  • $\begingroup$ Highly recommended by me, too. $\endgroup$ – Michael Lew Sep 21 '11 at 1:28
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Schaeffer's book from Duxbury press seems ok. Sheldon Ross' books are always awesome. Note, these are both books on Probability, not stats, which is what you asked.

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I'd strongly recommend Bulmer's Principles of Statistics as a leaping-off point. It's a touch dated, but it's short, clear and available in a cheap Dover edition - around $10 from Amazon. For a more modern and to the point statistical book I'd suggest Wasserman's "All of Statistics". I got it a few months back and it's been a good survey of everything - I've not read the first few chapters in detail but it seems ok on a skim. I like some of the practical advice which would be useful in a self study context - e.g. "Unbiasdness used to receive much attention but these days is considered less important".

But this is assuming you want a practical statistics text which covers some probabilty rather than a probability theory text. For probability theory, I'd suggest reading a lot on measure theory and hit something on Lebegue integration first - but this doesn't sound like where you're at.

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    $\begingroup$ I used Wassermann's book to supplement the official one that every other instructor in a ten-section "Intro to Stats for Engineers" class was obliged to use, and liked it way better than the required textbook. It swoops through statistics at an amazing pace by omitting all the proofs, in the hope that a mathematically savvy student will either see through it, or consult more rigorous books. $\endgroup$ – StasK Sep 21 '11 at 15:45
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https://www.crcpress.com/Introduction-to-Probability/Blitzstein-Hwang/p/book/9781466575578 - Introduction to Probability

I had no experience in probability before; this is a good book that explains the basic probability distributions with motivating context. Begins with discrete random variables and moves to continuous, which is good for the beginner. Builds your foundation up so you can tackle more advanced topics in the future.

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