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

"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. 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."--BOOK JACKET.  Read more... 1. Why probability and statistics? -- 2. Outcomes, events, and probability -- 3. Conditional probability and independence -- 4. Discrete random variables -- 5. Continuous random variables -- 6. Simulation -- 7. Expectation and variance -- 8. Computations with random variables -- 9. Joint distributions and independence -- 10. Covariance and correlation -- 11. More computations with more random variables -- 12. The Poisson process -- 13. The law of large numbers -- 14. The central limit theorem -- 15. Exploratory data analysis : graphical summaries -- 16. Exploratory data analysis : numerical summaries -- 17. Basic statistical models -- 18. The bootstrap -- 19. Unbiased estimators -- 20. Efficiency and mean squared error -- 21. Maximum likelihood -- 22. The method of least squares -- 23. Confidence intervals for the mean -- 24. More on confidence intervals -- 25. Testing hypotheses : essentials -- 26. Testing hypotheses : elaboration -- 27. The t-test -- 28. Comparing two samples