## Statistics: Problems and SolutionsOriginally 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 |

217 | |

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### Common terms and phrases

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