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Sveshnikov A.A. Problems in Probability Theory, Mathematical Statistics and Theory of Random Functions

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Sveshnikov A.A. Problems in Probability Theory, Mathematical Statistics and Theory of Random Functions
Dover Publications, 1979. — 491 p. — ISBN: 0486637174, 9780486637174
Series: Dover Books on Mathematics
Sveshnikov gives a very brief introduction to each topic, with definitions and formulae presented without proofs, followed by a couple of worked examples, and a couple pages of problems. Answers to all problems are in the back, making it ideal for self-study.
If you have not studied any statistics before, you might want to start with a book that gives more explanation, such as Bulmer, "Principles of Statistics."
This book makes use of calculus in many sections. For interesting probability problems with less advanced math, you might try Mosteller, "Fifty Challenging Problems in Probability."
If you take the time to work through a number of problems from each chapter, you can learn how to apply probability and statistics to a wide variety of problems. The equations I derived for the thesis I'm working on are the topic of chapter 6!
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