## Statistics: Problems and SolutionsWhat 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 |

217 | |

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