# Statistics: Problems and Solutions

World Scientific, 2000 - Mathematics - 227 pages
Originally published in 1986, this book consists of 100 problems in probability and statistics, together with solutions and, most importantly, extensive notes on the solutions. The level of sophistication of the problems is similar to that encountered in many introductory courses in probability and statistics. At this level, straightforward solutions to the problems are of limited value unless they contain informed discussion of the choice of technique used, and possible alternatives. The solutions in the book are therefore elaborated with extensive notes which add value to the solutions themselves. The notes enable the reader to discover relationships between various statistical techniques, and provide the confidence needed to tackle new problems.

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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