Page 14 - Probability and Statistical Inference

Preface vii

Obviously there are competing textbooks at this level. What sets this
book apart from the others? Let me highlight some of the novel features
of this book:
1. The material is rigorous, both conceptually and mathematically, but I
have adopted what may be called a “tutorial style.” In Chapters 1-12, the
reader will find numerous worked examples. Techniques and concepts are
typically illustrated through a series of examples and related exercises,
providing additional opportinities for absorption. It will be hard to find another
book that has even one-half the number of worked examples!
2. At the end of each chapter, a long list of exercises is arranged according
to the section of a concept’s origin (for example, Exercise 3.4.2 is the second
exercise related to the material presented in Section 3.4). Many exercises
are direct follow-ups on the worked-out examples. Hints are frequently
given in the exercises. This kind of drill helps to reinforce and emphasize
important concepts as well as special mathematical techniques. I have found
over the years that the ideas, principles, and techniques are appreciated
more if the student solves similar examples and exercises. I let a reader
build up his/her own confidence first and then challenge the individual to
approach harder problems, with substantial hints when appropriate. I try to
entice a reader to think through the examples and then do the problems.
3. I can safely remark that I often let the examples do the talking. After
giving a series of examples or discussing important issues, I routinely
summarize within a box what it is that has been accomplished or where one
should go from here. This feature, I believe, should help a reader to focus
on the topic just learned, and move on.
4. There are numerous figures and tables throughout the book. I have
also used computer simulations in some instances. From the layout, it should
be obvious that I have used the power of a computer very liberally.
I should point out that the book contains unique features throughout. Let
me highlight a few examples:
a) In Section 2.4, the “moment problem” is discussed in an elementary
fashion. The two given density functions plotted in Figure 2.4.1 have identical
moments of all orders. This example is not new, but the two plots certainly
should grab one’s attention! Additionally, Exercise 2.4.6 guides a reader in
the construction of other examples. Next, at this level, hardly any book
discusses the role of a probability generating function. Section 2.5 does
precisely that with the help of examples and exercises. Section 3.5 and
related exercises show how easily one can construct examples of a collection
of dependent random variables having certain independent subsets within