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I'm looking for a good textbook introduction to probability/statistics that a first/second year undergrad math student could use! I'd like a book that emphasizes theory over procedure. I'd prefer an open-source textbook, but I'm willing to pay if you believe it is worth the money.

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I found http://www.randomservices.org/random/ useful. It is written in a formal language, but it has examples, exercises and also interactive demonstrations/illustrations.

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  • $\begingroup$ Seconding this recommendation: I took a look at a few pages and find this reference rather thoughtfully curated. $\endgroup$
    – Ryan G
    Mar 3 at 6:43
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http://fstroj.uniza.sk/kam/orsansky/pdf/eng/basicsofstatisticalmethods.pdf

The pdf of this book contains :

  1. Probability theory
  2. Random variable
  3. Significant continuous distribution of a random variable
  4. Descriptive statistics
  5. Estimates of parameters
  6. Testing statistical hypotheses
  7. Correlation Analysis
  8. Paired linear regression

This book covers the maximum syllabus of the first/second year of undergrad mathematics/statistics syllabus. This book was suggested by my professors. I'm a third-year undergraduate statistics student. I hope this helps!

While studying things online, I came across this book :

Naked Statistics: Stripping the Dread from the Data [ Book by Charles Wheelan ]

This book was successful in filling in the conceptual gaps of my understanding of statistics. So, if you are looking for some book that clears your concepts of statistics, this is a good read. I ordered the hard copy since I didn't found the opensource for this yet, but if I will get, I'll share the link here.

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Have you tried the MAA's book reviews? You can filter by topic and rating. Because you prefer "a book that emphasizes theory over procedure", try Probability Theory as well as Probability.

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I have used this one. It's adequate and free!

https://saylordotorg.github.io/text_introductory-statistics/

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