Probability and Statistics
The revision of this well-respected text presents a balanced approach of the classical and Bayesian methods and now includes a chapter on simulation (including Markov chain Monte Carlo and the Bootstrap), coverage of residual analysis in linear models, and many examples using real data. Calculus is assumed as a prerequisite, and a familiarity with the concepts and elementary properties of vectors and matrices is a plus.
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Review: Probability and StatisticsUser Review - Ben - Goodreads
Best book I have read on both subjects. Just the right amount of math for someone that knows calc (doesn't need a hand held), but isn't a mathematicians (very simple proofs). Read full review