Corrections to Probability and Statistics
(Third Edition)

This file was last updated January 29, 2010
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## Contents

### Preface

• p. xv: I forgot to thank Valerie Ventura, who read an early draft of Section 11.5. (10/22/01)

### Chapter 1

Section 1.1
Section 1.2
Section 1.3
Section 1.4
Section 1.5
Section 1.6
Section 1.7
Section 1.8
Section 1.9
Section 1.10
• p. 41, Theorem 1.10.2, line 2:  '' should be  ''. (7/9/02)
Section 1.11
Section 1.12

### Chapter 2

Section 2.1
• p. 52, Theorem 2.1.1: Remove the words  and'' from the statement. (6/13/02)
• p. 53, Theorem 2.1.2: Also assume that . (10/12/01)
Section 2.2
• p. 59, line : exactly two nondefectives'' should read exactly two defectives''. (9/5/02)
Section 2.3
• p. 76, line 9: Example 2.3.2'' should read Example 2.3.10''. (10/18/02)
• p. 76, in Example 2.3.11, the third line of the table should read
 Prior prob. 0 0.19 0.19 0.17 0.14 0.11 0.09 0.06 0.04 0.01 0

(9/8/03)
• p. 76, Figure 2.4 caption line 2: 25'' should read 40'' (10/18/02)
• p. 78, Exercise 18: Assume that . (10/12/01)
Section 2.4
Section 2.5
Section 2.6

### Chapter 3

Section 3.1
• p. 101 On line 5 of the NOTE:  '' should be  ''. (5/14/07)
Section 3.2
Section 3.3
Section 3.4
Section 3.5
• p. 136 Exercise 8: add the condition to the first branch of the definition of . (2/15/02)
Section 3.6
Section 3.7
• p. 153, equation (3.7.10): for '' should read for '' (10/22/04)
• p. 154, second displayed equation: '' should read ''. (12/28/09)
• p. 155, last line:  '' should read  '' (10/22/07)
• p. 157 Exercise 3 line 5: for '' should read for '' (1/25/02)
Section 3.8
• p. 164, Exercise 5, in the displayed equation, '' should be '' (2/5/07)
• p. 164, Exercise 12, line 3: page 114'' should read page 115'' (10/12/01)
• p. 164, Exercise 14: Assume that . (1/28/02)
Section 3.9
• p. 176, Exercise 18 line2: for '' should read for '' (10/12/01)
Section 3.10

### Chapter 4

Section 4.1
• p. 189 Exercise 14(b) line 3: loses '' should read loses '' (10/12/01)
Section 4.2
Section 4.3
Section 4.4
Section 4.5
Section 4.6
• p. 221, Exercise 8 in displayed equation:  '' should read  ''. (4/7/03)
Section 4.7
• p. 227, Figure 4.8: In the legend, the solid line should be labelled Marginal'' and the dotted line should be labelled Conditional''. (10/15/01)
Section 4.8
• p. 232, last line of Example 4.8.2: '' should read  '' (5/15/03)
Section 4.9
Section 4.10

### Chapter 5

Section 5.1
Section 5.2
Section 5.3
Section 5.4
Section 5.5
Section 5.6
• p. 273, Example 5.6.4 line 2: interested finding'' should read interested in finding'' (6/25/03)
• p. 277, Example 5.6.7 line 10: Then then'' should read Then'' (2/25/03)
Section 5.7
• p. 284, line 13:  '' should read  '' (6/4/03)
• p. 284, line 15: no more that 1/4'' should read no more than 1/4'' (2/25/03)
• p. 291, Exercise 14: In both parts (a) and (b), the lower limit of summation should be '' rather than ''. (10/12/01)
Section 5.8
Section 5.9
• p. 302, Exercise 16, displayed equation (numerator): '' should read '' (4/7/03)
Section 5.10
• p. 304, line 8: Eq. (5.10.2)'' should refer to the unnumbered displayed equation in lines 2 and 3 of the page. (11/1/07)
Section 5.11
Section 5.12
• p. 315, Eq. (5.12.6): '' should read ''. (10/22/01)
• p. 319, Exercise 4, line 4: his'' should be her''. (11/17/02)
Section 5.13

### Chapter 6

Section 6.1
Section 6.2
Section 6.3
• p. 341, Example 6.3.5, line 9: distribution of '' should read distribution of '' (2/25/03)
• p. 342, line 1:  '' should read  '' (4/7/03)
Section 6.4
• p. 351, Example 6.4.5, line 7: Eq. (3.6.1)'' should read Eq. (6.3.1)'' (2/21/03)
Section 6.5
• p. 361, last line: Exercise 6'' should read Exercise 10'' (10/29/07)
• p. 363, in the hint for Exercise 10: when the distribution is specified in Exercise 1'' should read as in Theorem 4.5.1'' (7/17/09)
Section 6.6
Section 6.7
Section 6.8
Section 6.9
• p. 385, line 7: (6.9.3)'' should read (6.9.4)''. (8/5/09)
Section 6.10

### Chapter 7

Section 7.1
Section 7.2
Section 7.3
Section 7.4
Section 7.5
Section 7.6
• p. 420, Eq. (7.6.8):  '' should read  ''. (4/7/03)
• p. 426, line 8: probability '' should read probability ''. (4/7/03)
Section 7.7
Section 7.8
Section 7.9
• pp. 446-447, Exercises 14-23: Shortly before the text went to press, the Exercises 13(b) through 22 got renumbered as 14-23. That is, Exercise 14 is supposed to be Exercise 13(b), and 15-23 are supposed to be 14-22. The answers on page 793 that are labeled 15 and 21 are now answers to Exercises 16 and 22. I don't know how this renumbering happened. (10/12/01)

### Chapter 8

Section 8.1
• p. 453, Example 8.1.3, line 6: Example 6.5.15'' should read Example 6.5.5'' (10/9/02)
• p. 462 Exercise 11: '' should read '' at the ends of parts b and c. (4/7/03)
Section 8.2
Section 8.3
Section 8.4
Section 8.5
• p. 486, Figure 8.8 caption: first '' should read ''. (7/24/09)
• p. 492, line 26:  '' should read  ''. (2/8/08)
Section 8.6
• p. 500, line : then '' should read then ''. (4/7/03)
Section 8.7
Section 8.8
• p. 518, last line of Example 8.8.1: '' '' should read ''- '' (7/16/09)
• p. 521, 2 and 4 lines after (8.8.16): In both places,  '' should read  '' (4/7/03)
Section 8.9
Section 8.10

### Chapter 9

Section 9.1
Section 9.2
Section 9.3
Section 9.4
• p. 559, line 5 of Example 9.4.1: quantile of'' should read quantile of the'' (3/20/08)
Section 9.5
Section 9.6
Section 9.7
• p. 577, last displayed equation: '' should be ''. (1/5/10)
Section 9.8
• p. 588, second line after (9.8.1): '' should be ''. (1/6/10)
• p. 589, second line of Example 9.8.1: intereted'' should be interested''. (3/26/08)
• p. 591, first line of text: signed ranks test'' should read ranks test''. (4/7/03)
• p. 593, Eq. (9.8.6): The correct formula is

(11/26/01)
• p. 595, Exercise 15: There are a few errors in the statement of the problem. The corrected exercise is given here:
15.
Consider again the conditions of Exercise 1. This time, let . Wilcoxon (1945) developed the following test of the hypotheses (9.8.7). Order the absolute values from smallest to largest, and assign ranks from 1 to to the values. Then is set equal to the sum of all the ranks of those such that . If the distribution of is symmetric around 0, then the mean and variance of are

The test rejects if , where is chosen to make the test have level of significance . This test is called the Wilcoxon signed ranks test. If is large, a normal distribution approximation allows us to use .
a.
Let if the that gets rank has and if not. Show that .
b.
Prove that is as stated in Eq. (9.8.8) under the assumption that the distribution of is symmetric around 0. Hint: You may wish to use Eq. (4.7.13).
c.
Prove that is as stated in Eq. (9.8.9) under the assumption that the distribution of is symmetric around 0. Hint: You may wish to use Eq. (4.7.14).
(11/26/01)
Section 9.9

### Chapter 10

Section 10.1
• p. 606, second line after (10.1.12):  '' should read  ''. (4/7/03)
Section 10.2
• p. 610, in (10.2.1): '' should read ''. (1/29/10)
• p. 614, 3rd displayed equation:  '' should read  ''. (4/7/03)
• p. 615, Example 10.2.3, line 4:  '' should read  '' (4/7/03)
Section 10.3
• p. 619, first line after (10.3.2):  '' should read  ''. (4/7/03)
• p. 633, last line of (10.3.27): '''' should read ''. (1/29/10)
• p. 634, Eq. (10.3.28), end of first line:  '' should read ''. (4/7/03)
• p. 638, Exercise 22: The problem should have asked for the regression of logarithm of 1980 price on the logarithm of 1970 price. It can be solved either as stated here or as stated in the text, but the regression on logarithm of 1970 price makes more sense. (12/14/01)
Section 10.4
• p. 639, end of second to last displayed equation:  '' should read  ''. (4/7/03)
• p. 640, two lines after (10.4.6): '' should read ''. (4/7/03)
• p. 641, first line after (10.4.7): 15 degrees of freedom'' should read 14 degrees of freedom''. (4/7/03)
• p. 644, first line of text: 7.191'' should read 7.181''. (4/7/03)
Section 10.5
• p. 650, Example 10.5.2, end of first displayed equation: 144.1'' should read 172.3''. (4/7/03)
• p. 652, three lines before Example 10.5.3: '' should read  ''. (4/7/03)
• p. 658, last displayed equation:  '' should read  ''. (4/7/03)
• p. 661, line :  '' should read  ''. (4/7/03)
• p. 662, Exercise 2, line 2:  has a '' should be  has a ''. (12/16/01)
Section 10.6
• p. 668, line 5: Eq. (10.6.7) has a'' should read Eq. (10.6.7), when divided by , has a''. (4/7/03)
• p. 672, Exercise 2, displayed equation: Both places where appears in a denominator should be . (4/7/03)
• p. 673, Exercise 14(a):  '' should be  '' (12/17/01)
Section 10.7
• p. 680, line 6: The typo'' that had been listed here was actually correct as stated in the book. (7/9/08)
Section 10.8
Section 10.9

### Chapter 11

Section 11.1
• p. 702, line : estimate parameter'' should read estimate a parameter'' (10/12/01)
• p. 711 Exercise 1 line 9:  '' should read  '' (12/19/01)
Section 11.2
• p. 714, first row of last displayed equation:  '' should read  ''. (4/7/03)
• p. 722, Example 11.2.10, last line: is'' should read if''. (4/7/03)
Section 11.3
Section 11.4
• p. 748, last displayed equation: The equation should read

(4/7/03)
• p. 752, column 1 line 3: variance '' should read precision '' (1/3/02)
• p. 752, Exercise 13(a): The 1/2'' exponent should be '' in the displayed formula. (1/3/02)
• p. 752, Exercise 14: Add the text The prior hyperparameters are , , , and .'' (1/4/02)
• p. 753, Exercise 15 part a line 2: Delete the text if , then'' (1/4/02)
• p. 753, Exercise 15 part b line 2: Delete the text if , then'' (1/4/02)
Section 11.5
Section 11.6
• p. 767, Exercise 12 line 7: (8.6.9)'' should read (8.6.3)'' (1/6/02)
• p. 767, Exercise 13(b) line 2: '' should read '' (1/7/02)
• p. 767 Exercise 16: The displayed formula should read

(1/7/02)

### References

• p. 782, Exercise 5 in Section 1.9: '' should be '' (7/9/02)
• p. 782, The answer to 13.(d) that appears in Section 1.10 should appear in Section 1.12. (7/9/02)
• p. 782, Exercise 11.(a) in Section 2.2: 0.25'' should read 0.2617'' (7/9/02)
• p. 790, line 6, answer to 29: '' should read  ''. (4/7/03)
• p. 792, Section 7.6, answer to 9: (a)(7.084,7.948); (b)(7.031,7.969)'' should read (a)(157.8,210.1); (b)(152.6,211.8)'' (4/7/03)
• p. 793, lines 3-4: The answers labeled 15 and 21 are actually answers to Exercises 16 and 22 due to the mysterious renumbering that was described above for pages 446-447. (10/12/01)
• p. 793, Section 8.1, answer to 11.(a): '' should read ''. (4/7/03)
• p. 793, Section 8.1, answer to 11.(b): 0.0956'' should read 0.0994''. (4/7/03)
• p. 794, Exercises 11(a) and 11(b) in Section 8.6: Both should be Don't reject .'' (11/9/01)
• p. 795, Exercise 17 in Section 9.7:  '' should read  ''. (4/7/03)
• p. 795, Exercise 1 in Section 9.9: (322,440)'' should be (141,175)''. (12/12/01)
• p. 799, Exercise 5 in Section 11.4 should read Approximation = 0.2542, sim. std. err. = .'' (1/3/02)
• p. 799, Exercise 7 in Section 11.4: 825.8'' should be 826.8'' (1/3/02)