A Natural Introduction to Probability Theory [Paperback]

According to Leo Breiman (1968), probability theory has a right and a left hand. The right hand refers to rigorous mathematics, and the left hand refers to pro- bilistic thinking. The combination of these two aspects makes probability theory one of the most exciting ?elds in mathematics. One can study probability as a purely mathematical enterprise, but even when you do that, all the concepts that arisedo haveameaningontheintuitivelevel.Forinstance,wehaveto de?newhat we mean exactly by independent events as a mathematical concept, but clearly, we all know that when we ?ip a coin twice, the event that the ?rst gives heads is independent of the event that the second gives tails. Why have I written this book? I have been teaching probability for more than ?fteen years now, and decided to do something with this experience. There are already many introductory texts about probability, and there had better be a good reason to write a new one. I will try to explain my reasons now.Experiments.- Random Variables and Random Vectors.- Random Walk.- Limit Theorems.- Intermezzo.- Continuous Random Variables and Vectors.- Infinitely Many Repetitions.- The Poisson Process.- Limit Theorems.- Extending the Probabilities.

The book [is] an excellent new introductory text on probability. The classical way of teaching probability is based on measure theory. In this book discrete and continuous probability are studied with mathematical precision, within the realm of Riemann integration and not using notions from measure theory&. Numerous topics are discussed, such as: random walks, weak laws of large numbers, infinitely many repetitions, strong laws of large numbers, branching processes, weak convergence and [the] central limit theorem. The theory is illustrated with many original and surprising examples and problems.

ZENTRALBLATT MATH

Most textbooks designed for a one-year course in mathematical statistics coló×