Probability and Statistics

By zhao bin

This book bridges abstract theory and real-world application, serving as a foundational resource for students and practitioners in probability, statistics, and data science. It addresses the philosophical challenge of navigating a non-deterministic world by distinguishing probability (deductive, mathematical "known") from statistics (inductive, scientific "unknown"). Part I: The Machinery of Probability formalizes chance through axioms, sample spaces, and set theory. Conditional probability reshapes perspective by updating beliefs with new information, leading to independence/dependence concepts. Bayes' Theorem is highlighted as a revolutionary tool for hypothesis updating. Random variables (discrete/continuous) and distributions (Binomial, Poisson, Normal) are explored, with the Normal distribution emphasized via the Central Limit Theorem for its ubiquity in inference. Expectation is introduced for risk assessment. Part II:: The Practice of Inference applies theory to draw population conclusions from samples. Sampling concepts (bias, variability, randomization) and sampling distributions underpin uncertainty quantification. Confidence intervals (interpreting "95% confidence") and hypothesis testing (p-values, Type I/II errors) are explained conceptually, warning against misinterpretation pitfalls. Exploring Relationships and Advanced Applications extends to multivariate analysis via correlation and regression. Linear regression models relationships, with slope/intercept interpretation, R-squared for fit assessment, and assumption checks. The book concludes with modern applications (machine learning, A/B testing) and ethical considerations, stressing statistical literacy to combat misuse. Ultimately, the text cultivates a mindset embracing uncertainty, evidence-based reasoning, and quantified doubt, empowering readers to navigate incomplete information with rigorous intellectual tools.

• Format: Paperback
• Language: English
• ISBN: 9999356745
• ISBN13: 9789999356749
• Release Date: September 2026
• Publisher: Eliva Press
• Length: 430 Pages
• Weight: 1.27 lbs.
• Dimensions: 9.0" x 1.0" x 6.0"