Statistics: Problems and Solutions

World Scientific, 2000 - Mathematics - 227 pages
What is most valuable about this book is the very high quality of the model solutions It is a problem book for those teaching or learning a first course in mathematical statistics This one is outstandingly good and highly recommended.Goeff CohenUniversity of Edinburgh, ScotlandThe authors of this useful book take the view that the ability to solve practical problems is fundamental to an understanding of statistical techniques The book is designed to be read alongside a standard text. I expect it is likely to be most useful to the teacher or to the able student forced to work largely alone.David GreenThis book not only provides a solution to each problem set but gives notes about that solution. These notes should help students to understand the reasoning behind the techniques used, so giving them confidence to deal with problems of a similar nature This book should prove a valuable addition to the library of students and teachers of statistics.M J G AnsellHatfield PolytechnicThe book consists of aseries of examples, each followed by one or more alternative solutions and accompanying notes. The solutions themselves are useful models. The notes go one stage further and explain why particular techniques were chosen to solve each problem. This approach may help to overcome the common difficulty of deciding which method to choose when answering examination questions The book is easy to read and suitable for individual study.Richard J FieldThese notes provide fascinating insights into the process that experienced statisticians go through in order to solve a problem. Students (and maybe some instructors) will benefit greatly from going through the solutions and the notes in thisbook.Gudmund R IversenSwarthmore CollegeThe approach of the authors is to improve a students understanding of statistics, and to help students appreciate which techniques might be appropriate for any problem.Zentralblatt Math., 2001

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Contents

 Preface Probability and Random Variables 1 The Wellington boots 2 Dealing four cards 4 The school assembly 7 The second card 10 Winning at craps 14 The fisherman 16 Testing lightbulbs 18
 Fitting plungers into holes 75 Bird wingspans 77 Distributions related to the Normal 78 Failures of belt drives 79 Guaranteed life of a machine 81 Watch the birdie 82 Breaking a rod at random 85 2C Simulating Random Variables 88

 Designing a navigation system 19 The sports club 20 Playing the fruit machine 24 IB Random Variables 25 The highest score in a dice game 26 The total score from two dice 27 Selecting balls from an urn 30 The game of darts 32 The randomised response experiment 35 Finding a probability density function 36 Positioning the pointer 37 Finding the mode and median of a distribution 39 Buffons needle 42 Transforming a random variable 43 Length of a chord of a circle 45 Probability Distributions 47 The squash match 48 Sampling incoming batches 49 Sampling for defective items 51 The music recital 52 Marking a multiplechoice test 54 The insect breeding experiment 55 The telephone exchange 57 Random sultanas in scones 59 Relationship between binomial and Poisson distributions 61 Tossing a coin untilheadsappears 63 Estimating the size of a fish population 65 Collecting cigarette cards 67 2B Continuous Distributions 70 Mixing batches of pesticide 71 Tolerances for metal cylinders 72 The number of matches in a box 74
 Using dice to obtain random numbers 90 Ants on flower heads 92 Data Summarisation and GoodnessofFit 95 The weights of club members 96 Histogram for catches of fish 100 Distribution of examination marks 102 Consumption of cigarettes 103 3B GoodnessofFit 105 Numbers of sixes in dice throws 106 The occurrences of thunderstorms 107 The distribution of I O 110 Frontal breadths of skulls 113 Rotating bends 115 Distribution of accidents in a factory 117 Inference 120 Lengths of manufactured bolts 121 Lifetimes of electrical components 123 The diameters of marbles 125 Variability in weight of bottled fruit 126 Changes in weight of manufactured product 127 Estimating the mean and variance 129 Normal Distribution 130 Experimental teaching of arithmetic 134 Milk yield of cows 136 4C Binomial and Poisson Distributions 145 4D Other Problems 158 Analysis of Structured Data 176 5B Analysis of Variance 194 5C Contingency Tables 202 5D Time Series 210 Index 217 Copyright