Probability and Statistics for Data Science Math + R + Data by Norman S. Matloff

Probability and Statistics for Data Science: Math] R + Data covers "math stat"-distributions, expected value, estimation etc.-but takes the phrase "Data Science" in the title quite seriously:

* Real datasets are used extensively.

* All data analysis is supported by R coding.

* Includes many Data Science applications, such as PCA, mixture distributions, random graph models, Hidden Markov models, linear and logistic regression, and neural networks.

* Leads the student to think critically about the "how" and "why" of statistics, and to "see the big picture."

* Not "theorem/proof"-oriented, but concepts and models are stated in a mathematically precise manner.

Prerequisites are calculus, some matrix algebra, and some experience in programming.

Norman Matloff is a professor of computer science at the University of California, Davis, and was formerly a statistics professor there. He is on the editorial boards of the Journal of Statistical Software and The R Journal. His book Statistical Regression and Classification: From Linear Models to Machine Learning was the recipient of the Ziegel Award for the best book reviewed in Technometrics in 2017. He is a recipient of his university's Distinguished Teaching Award.