A Modern Introduction to Probability and Statistics : Understanding Why and How

F.M. Dekking, C. Kraaikamp, H.P. Lopuhaä, L.E. Meester




Probability and Statistics are studied by most science students, usually as a second- or third-year course. Many current texts in the area are just cookbooks and, as a result, students do not know why they perform the methods they are taught, or why the methods work. The strength of this book is that it readdresses these shortcomings; by using examples, often from real-life and using real data, the authors can show how the fundamentals of probabilistic and statistical theories arise intuitively. It provides a tried and tested, self-contained course, that can also be used for self-study.

A Modern Introduction to Probability and Statistics has numerous quick exercises to give direct feedback to the students. In addition the book contains over 350 exercises, half of which have answers, of which half have full solutions. A website at www.springeronline.com/1-85233-896-2 gives access to the data files used in the text, and, for instructors, the remaining solutions. The only pre-requisite for the book is a first course in calculus; the text covers standard statistics and probability material, and develops beyond traditional parametric models to the Poisson process, and on to useful modern methods such as the bootstrap.

This will be a key text for undergraduates in Computer Science, Physics, Mathematics, Chemistry, Biology and Business Studies who are studying a mathematical statistics course, and also for more intensive engineering statistics courses for undergraduates in all engineering subjects.


Table of contents

Why Probability and Statistics?- Outcomes, Events and Probability.- Conditional Probability and Independence.- Discrete Random Variables.- Continuous Random Variables.- Simulation.- Expectation and Variance.- Computations with Random Variables.- Joint Distributions and Independence.- Covariance and Correlation.- More Computations with More Random Variables.- The Poisson Process.- The Law of Large Numbers.- The Central Limit Theorem.- Exploratory Data Analysis: Graphical Summaries.- Exploratory Data Analysis: Numerical Summaries.- Basic Statistical Models.- The Bootstrap.- Unbiased Estimators.- Efficiency and Mean Squared Error.- Maximum Likelihood.- The Method of Least Squares.- Confidence Intervals for the Mean.- More on Confidence Intervals.- Testing Hypotheses: Essentials.- Testing Hypotheses: Elaboration.- The t-test.- Comparing Two Samples.- Datasets.- Appendix A: Answers to Selected Exercises.- Appendix B: Solutions to Selected Exercises.- References.- Index.