Introduction to probability. 2nd rev. ed. (English) Zbl 0914.60004
Providence, RI: American Mathematical Society (AMS). 510 p. (1997).
The book is a beautiful introduction to probability theory at the beginning level. It has twelve chapters covering all essential material required for science and engineering students. The book contains a lot of examples and an easy development of theory without any sacrifice of rigor, keeping the abstraction to a minimal level. Chapters 1 and 2 deal with discrete and continuous random variables with appropriate distribution and density functions. The next chapter is devoted to combinatorics. Each section has at least two examples and enough exercises. Chapter 4 introduces a very important topic of conditional probability. Some important distributions and densities are given in Chapter 5. First and second order statistics are discussed in the next chapter. Chapters 7, 8 and 9 are related to independent random variables and central limit theorems. The authors describe generating functions for discrete and continuous random variables. This chapter also has advanced topic – branching processes. The last two chapters – “Markov chains” and “Random walks” – are usually covered in advanced courses and are very important for stochastic process and communications systems. It has three appendices (standard tables). It is indeed a valuable addition to the study of probability theory.
Reviewer: N.C.Mohanty (Huntington Beach)
MSC:
60-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory |
Keywords:
distribution and density functions; conditional probability; order statistics; central limit theorems; generating functions; branching processesOnline Encyclopedia of Integer Sequences:
Triangle read by rows: T(n,k) is the number of walks (each step +-1) of length 2n which have a cumulative value of 0 last at step 2k.Triangle read by rows: T(n,k) = the number of ascending runs of length k in the permutations of [n] for k <= n.
Number of runs or rising sequences of length 2 among all permutations of n.