In Spring 2010 I used this book to teach a calculus-based undergraduate course in statistics and probability at Metropolitan State University in Saint Paul. I covered chapters 1, 2, 3, 4, 6, 7, 12 and 13.



In short, I cannot recommend the book. Explanations are often verbose and hard to follow, there are no problem solutions in the back of the book, and there is a plethora of typos and more serious mistakes throughout the book. Below is a detailed list of the mistakes I found in the first printing of the first edition. It is to be hoped that these will be corrected in later printings.



The numbers of many problems haven't been checked, often leading to outrageous and unrealistic probabilities or p-values etc. Examples are the problems 4.1.8, 4.1.9, 4.1.10, 4.1.13, 4.1.14, 4.4.5, 4.4.6, 7.1.6, 7.4.8, 7.4.12, 7.4.15, 7.5.5, 7.6.3, 7.6.4, 12.4.7.



P.8 Definition 1.3.1 falsely asserts that if every element of the population has the same chance of being chosen, then every size n subset is equally likely.



P.27 Definition 1.5.2 for upper and lower quartile is incorrect (or at least unclear) in the case of several identical data items.



P.67 Birthday paradox example, final answer for n=40 is wrong.



P.73 Example 2.4.3 notation and concept of "genetic makeup" and "allele" are not sufficiently explained for non-biologists.



P.77 Step three of Bayes' Rule: "denominator probability" is not explained; the rule as written is not clear.



P.83 Problem 2.6.29 Variable i is used twice. "Head ith probability p" is unclear.



P.85 Line 5: "for all real values x of X" should be "for all real numbers"; this is the whole point of the sentence.



P.90 Problems 2.5.2 and 2.5.3 use the terms "probability function" and "distribution"; should be "probability mass function". 2.5.4 should not use the notation p(x) for the cdf.



P.91 Problem 2.5.5 No random variable can have the given cdf, since it isn't right continuous.



P.95 Definition 2.6.3 The crucial difference between E((X-mu)^2) and (E(X-mu))^2 is obscured by writing E(X-mu)^2. The definition is not clear. Ambiguous notations such as E(X-mu)^2, EX^2, E(X-my)^3 and E(X-muX)(Y-muY) are used throughout the book.



P.106 Problem 2.6.8: variance 4 is not needed.



P.121 The Poisson approximation "rule of thumb" np=2 not needed. However it should be mentioned that Chebyshev's Theorem is only interesting for K>1.



P.166 Theorem 3.5.2 The notations X-bar and S_n have not been defined. In the proof, the undefined abbreviation "iid" is used (which also cannot be found in the index). However, the variables were not assumed to be iid.



P.168 Theorem 3.5.2 It should be emphasized that the central limit theorem has one important assumption: that the mean and variance be finite. On the other hand, the moment generating function is not needed for the statement.



P.169 Example 3.5.7 (b) assumption n=300 is missing. (c) what is n?



P.170 Example 3.5.8 is completely unclear. "such that they can be confident"? How confident? In the solution the confidence 0.99 appears out of the blue. The maximum of pq should be explained with calculus. The fundamental importance of this example needs to be explained: it is used to estimate any unknown probability, not just unfair coins.



P.172 Problem 3.5.4 This should be "number of cars arriving at a busy intersection in a given 20 minute interval".



P.173 All the problems from section 3.5 return later in section 4.1.



P.184 line 5: the normal distribution is not called "the theorem of de Moivre-Laplace".



P.185 Example 4.1.1 The last paragraph should not be part of the example.



P.186 Theorem 4.1.1 Was already used on p.167. The last sentence is Theorem 3.5.2.



P.187 Example 4.1.2 Cannot be solved at this point, needs Corollary 4.2.2!



P.213 "z-series" should be "z-scores"



P.215 "(a+0.5)" should be "(b+0.5)"



P.217 Problem 4.4.10 "90 heads" should be "at least 90 heads".



P.316 line 2: "we know that" should give a reference to the proper theorem.



P.328 Problem 6.5.9 "1997" and "1998" should be "2000" and "2001".



P.341 figure at the bottom: explain the meaning of the two distributions, "critical value" has not been explained.



Many hypothesis tests are taken to be one-tailed, without proper justification. In the real world, such justification is extremely rare.



While the text emphasizes the importance of computing p-values, the worked examples almost never show the computation of p-values.



The crucial difference between the size of an effect and the statistical significance of an effect is not sufficiently emphasized.



P.345 Example 7.1.5 is unrealistic, testing a null hypothesis of mu=15 against an alternative of mu=16. The value mu=16 should only be used to compute beta, not as alternative hypothesis.



P.346 The example is unintelligible, since mu_a is not explained.



P.349 Problem 7.1.5(c) beta=0.8 is completely unrealistic.



P.365 Top: Assumption n>=30 for the large sample case is incomplete: we also need finite variance!



P.373 Line 4: X_{1n_1}, X_{2n_2}



P.387 Problem 7.5.9: Cannot assume that the samples are independent; only part (c) makes any sense.



P.389 Top: Definitions of Q^2 is wrong; denominator should be np_i.



P.390 Box: "exact methods are available etc." is not an assumption.



P.390 Should point out the crucial logical issue here: if Q^2 is small, then we don't have enough evidence to reject H_0; this DOES NOT imply that we have evidence in favor of H_0! Same mistake in example 7.6.3.



P.391 "n=4" should be "k=4"; n is 500.



P.392 Section 7.6.2 Horrible language.



P.393 bottom of box: E_{ij} = n_{i.}n_{.j} (Same typo on p.394).



P.393 Explanation for the degrees of freedom formula (r-1)(c-1) is missing.



P.398 Problem 7.6.5 Where does H_0 come from? Does it talk about before or after advertising?



P.601 Line 6: "differing only in median or mean 3"??



P.602 The given approach for computing confidence intervals for the median is wrong. The median will be below X_{a+1} with probability alpha/2.



P.603 Example 12.2.1. Don't report this as a 95% confidence interval; state the correct confidence level instead.



P.607 Section 12.3.1 Assumption of continuous distribution should be stated first; no need to repeat P(X