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Full Description
The book provides a comprehensive technical foundation for understanding and analyzing data problems using quantitative empirical methods. It includes a thorough introduction to probability theory and statistics, followed by advanced concepts in quantitative empirical methods. The book also contains an elaborate appendix with all the mathematical techniques needed. Thus, the book is self-contained, requiring only high-school math as a prerequisite.
Concepts are explored through both theoretical presentations and practical examples, with formal technical proofs provided at the end of chapters. This structure makes the book suitable for undergraduate students wanting to learn and understand the concepts and to graduate students also wanting to prove various results to obtain even deeper insight.
Contents
1 Basic elements in probability theory 2 Distribution of a random variable 3 Joint distribution of random variables 4 Conditional distribution of a random variable 5 Aspects of a univariate distribution 6 Aspects of a multivariate distribution 7 Independence between random variables 8 Commonly used univariate distributions 9 Bivariate normal distributions 10 Distribution of a sample 11 Estimation theory 12 Estimating aspects of a univariate distribution 13 Estimation of a sampling distribution 14 Confidence intervals 15 Analysis of hypotheses 16 Test of hypotheses 17 Maximum likelihood estimation 18 Inference with maximum likelihood estimation 19 Bayesian methods 20 Appendix A: Probability theory 21 Appendix B: Real analysis 22 Appendix C: Simulation from a distribution
