Probability : An Introduction with Statistical Applications

Rating:
Summary: Probably the worst text I've ever bought
Review: I've yet to hear anyone speak positively about this text (including, at many points, my Statistics professor). (In all fairness, this particular book may have just been incredibly poorly selected for the course, which was the first Stats course the majority of the students had taken. At a higher level of statistical analysis, this text may be appropriate -- although, at that level, it may be perplexing as to why there are chapters on binomial distributions and approximating normals, etc., at all.)

At any rate, this text is NOT suited for introductory probabilistic or statistic analysis. It's a very notation-heavy and example-laden text, with very little appeal to intuition or worldly application. The individual sections rarely exceed 3 or 4 pages, in many cases leaving the student looking over the section in vain trying to find that important bit of knowledge they missed the first time around when it comes to doing the assigned problems at the end. The generating function chapter (5 pages, 2 of graphs), for instance, has a single straight-forward and painfully easy example -- rolling dice -- and then, in the supplementary questions, expects the student to discover Taylor polynomials for fractional exponent functions (or so I discovered upon asking the professor). Not only isn't there an example of this, there isn't even an allusion to the possibility of there being one. The entire class of 30 was bewildered. There is not one mention of Taylor polynomials within the chapter (not even to say they're sometimes necessary), or even a vague model for "discovering" generating functions from a series of numbers -- the only example works the other way (given generating function, find series). But perhaps it relies on knowledge pressupposed from other statistics course, in which case the fault lies on the professor.

Organizationally, this may be one of the hardest texts I've ever had to navigate. The blend of statistics and probability is confusing and ill-defined. The chapter on Geometric and Negative Binomial Distributions (probability-oriented) comes on the heels of Acceptance Sampling and Hypothesis Testing (statistical concepts), which comes on the heels of the Binomial Distribution. In practice, hypothesis testing has very little to do with probability (if you have a probabilistic model, you don't really need a hypothesis), and as a scientific concept requires statistic inferences that are no as of this point introduced. Other subtopics seem to be interspersed pretty well at random.

All in all, unless you have an incredibly high tolerance for statistic notation, and an incredible aptitude for seeing between the lines, this is not the book for you. The only redeeming chapter I found was on continuous functions. Otherwise, this text seems to presuppose far too much intuitive statistical understanding to be of any use to anyone but the most educated of statistians -- and I suspect those people have already found a better text in the first place.

Matty J

Rating:
Summary: Good Resource on Probability
Review: This is a rather unusual text. It covers most of the first half of a mathematical statistics course (which is 2 semesters long and requires the calculus sequence) which is on probability. This book does a nice job of covering all of the usual topics in probability in that sequence. The applications are to statistics, but are insufficient for a course in statistics. But these applications are well done and as such I think this book is a great resource for the student taking the mathematical statistics sequence. As for probability, I have taught a senior level course for math majors out of this text twice and intend to use it again. However, I did not have time to cover the applications to statistics (which I urge the students to study).

Rating:
Summary: Hard to follow
Review: To begin, I've read the author's preface so I know why Kinney wrote the book the way he did.

However, I find the explanations are hard to follow. I'm not the kind of student that has natural intuitions in mathematics and I need the step by step explanations that Kinney left out. I find that often times when the author summarizes with "It follows that", I don't follow.

Kinney's preface emphasizes the exploration of probability and a focus on solutions and their meanings as opposed to "mechanical effort". Yet, the problems require mechanical effort as well as mastery of the underlying principles.

The example problems are few and brief. One example left out so many details that I was amazed to learn all the other steps required to complete the problem.

The one thing I like about this book is that Kinney gives the odd numbered answers to the problems. But, I'd like to see all the answers because I don't think homework should be a test. Students have to show their work and when I'm working a problem, having the answer is often the only way I know that I'm using the right approach.