E-Book Content
Solutions Manual for Statistical Inference, Second Edition
George Casella University of Florida
Roger L. Berger North Carolina State University Damaris Santana University of Florida
0-2
Solutions Manual for Statistical Inference
“When I hear you give your reasons,” I remarked, “the thing always appears to me to be so ridiculously simple that I could easily do it myself, though at each successive instance of your reasoning I am baffled until you explain your process.” Dr. Watson to Sherlock Holmes A Scandal in Bohemia 0.1 Description This solutions manual contains solutions for all odd numbered problems plus a large number of solutions for even numbered problems. Of the 624 exercises in Statistical Inference, Second Edition, this manual gives solutions for 484 (78%) of them. There is an obtuse pattern as to which solutions were included in this manual. We assembled all of the solutions that we had from the first edition, and filled in so that all odd-numbered problems were done. In the passage from the first to the second edition, problems were shuffled with no attention paid to numbering (hence no attention paid to minimize the new effort), but rather we tried to put the problems in logical order. A major change from the first edition is the use of the computer, both symbolically through Mathematicatm and numerically using R. Some solutions are given as code in either of these languages. Mathematicatm can be purchased from Wolfram Research, and R is a free download from http://www.r-project.org/. Here is a detailed listing of the solutions included. Chapter 1 2 3 4
Number of Exercises 55 40 50 65
Number of Solutions 51 37 42 52
5
69
46
6 7
43 66
35 52
8 9
58 58
51 41
10 11 12
48 41 31
26 35 16
Missing 26, 30, 36, 42 34, 38, 40 4, 6, 10, 20, 30, 32, 34, 36 8, 14, 22, 28, 36, 40 48, 50, 52, 56, 58, 60, 62 2, 4, 12, 14, 26, 28 all even problems from 36 − 68 8, 16, 26, 28, 34, 36, 38, 42 4, 14, 16, 28, 30, 32, 34, 36, 42, 54, 58, 60, 62, 64 36, 40, 46, 48, 52, 56, 58 2, 8, 10, 20, 22, 24, 26, 28, 30 32, 38, 40, 42, 44, 50, 54, 56 all even problems except 4 and 32 4, 20, 22, 24, 26, 40 all even problems
0.2 Acknowledgement Many people contributed to the assembly of this solutions manual. We again thank all of those who contributed solutions to the first edition – many problems have carried over into the second edition. Moreover, throughout the years a number of people have been in constant touch with us, contributing to both the presentations and solutions. We apologize in advance for those we forget to mention, and we especially thank Jay Beder, Yong Sung Joo, Michael Perlman, Rob Strawderman, and Tom Wehrly. Thank you all for your help. And, as we said the first time around, although we have benefited greatly from the assistance and
ACKNOWLEDGEMENT
0-3
comments of others in the assembly of this manual, we are responsible for its ultimate correctness. To this end, we have tried our best but, as a wise man once said, “You pays your money and you takes your chances.” George Casella Roger L. Berger Damaris Santana December, 2001
Chapter 1
Probability Theory
“If any little problem comes your way, I shall be happy, if I can, to give you a hint or two as to its solution.” Sherlock Holmes The Adventure of the Three Students 1.1 a. Each sample point describes the result of the toss (H or T) for each of the four tosses. So, for example THTT denotes T on 1st, H on 2nd, T on 3rd and T on 4th. There are 24 = 16 such sample points. b. The number of damaged leaves is a nonnegative integer. So we might use S = {0, 1, 2, . . .}. c. We might observe fractions of an hour. So we might use S = {t : t ≥ 0}, that is, the half infinite interv