Statistics: Problems and Solutions

Front Cover
World Scientific, 2000 - Mathematics - 227 pages
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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
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