Basic Concepts Of Probability And Statistics Part 1

This book provides a mathematically rigorous introduction to the fundamental ideas of modern statistics for readers without a calculus background.

When as a practicing lawyer I published my ?rst article on statistical evidence in 1966, the editors of the Harvard Law Review told me that a mathematical equa- 1 tion had never before appeared in the review. This hardly seems possible - but if they meant a serious mathematical equation, perhaps they were right. Today all that has changed in legal academia. Whole journals are devoted to scienti?c methods in law or empirical studies of legal institutions. Much of this work involves statistics. Columbia Law School, where I teach, has a professor of law and epidemiology and other law schools have similar “law and” professorships. Many offer courses on statistics (I teach one) or, more broadly, on law and social science. The same is true of practice. Where there are data to parse in a litigation, stat- ticians and other experts using statistical tools now frequently testify. And judges must understand them. In 1993, in its landmark Daubert decision, the Supreme Court commanded federal judges to penetrate scienti?c evidence and ?nd it “re- 2 liable” before allowing it in evidence. It is emblematic of the rise of statistics in the law that the evidence at issue in that much-cited case included a series of epidemiological studies. The Supreme Court’s new requirement made the Federal Judicial Center’s Reference Manual on Scienti?c Evidence, which appeared at about the same time, a best seller. It has several important chapters on statistics.

Unlike traditional introductory math/stat textbooks, Probability and Statistics: The Science of Uncertainty brings a modern flavor to the course, incorporating the computer and offering an integrated approach to inference that includes the frequency approach and the Bayesian inference. From the start the book integrates simulations into its theoretical coverage, and emphasizes the use of computer-powered computation throughout. Math and science majors with just one year of calculus can use this text and experience a refreshing blend of applications and theory that goes beyond merely mastering the technicalities. The new edition includes a number of features designed to make the material more accessible and level-appropriate to the students taking this course today.