The book Probabilities and Statistics in Data Science concerns "mathematical statistics" (families of distributions, expected values, estimations of values, etc.), but puts particular emphasis on the aspect of "data science" included in the title:

With extensive use of datasets from real, everyday cases.

With programs written in the R language that support data analyses.

With references to many applications of data science, including, among others, principal component analysis (PCA), mixture distributions, random graph models, hidden Markov models, neural networks, as well as linear and logistic regression.

With appropriate guidance for students, helping them to critically examine the "how" and "why" of statistics and to see the big picture in each case.

With the formulation of concepts and models in a precise mathematical manner, but without being tied to the classic dichotomy of "statement of the theorem and proof."

The bibliography is intended for students with prerequisite knowledge of mathematical calculus and matrix algebra, as well as some experience in computer programming.

Contents:

• Basic probability models
• Monte Carlo simulation
• Discrete random variables: Expected value
• Discrete random variables: Variance
• Discrete parametric families of distributions
• Continuous probability models
• Statistics: Introduction
• Fitting continuous models
• The family of normal distributions
• Introduction to statistical inference
• Multivariate distributions
• The family of multivariate normal distributions
• Mixture distributions
• Multivariable data: Description and dimensionality reduction techniques
• Predictive modeling
• Model economy and overfitting
• Introduction to discrete-time Markov chains
• Quick introduction to R
• Matrix algebra