Probability and Statistics

This text confronts the conceptual difficulty many students have in learning probability and statistics by developing a precise foundation in concepts, working through theory, and then illustrating each concept with examples and applications directly related to the theory. The text explains the various interpretations of probability, the role of a model, and the importance of making a clear distinction between theoretical and empirical results. It defines a random variable "x" not on the real line but as a function with domain and abstract spaces. The book also introduces the notion of computer simulation and Monte Carlo methods, and argues that the controversy of Bayesian statistics has its origin in the dual interpretation of probability. Finally, there are chapters on the method of least squares, and the important topic of entropy.