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A Probability and Statistics Companion

by: Kinney, John J.

A Probability and Statistics Companion

by: Kinney, John J.

ISBN 13:
9780470471951
ISBN 10:
0470471956
Edition: 1st
Format: Paperback
Copyright: 06/09/2009
Publisher: Wiley

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Summary

Utilizing entertaining real-world examples, A Probability and Statistics Companion provides a unique, interesting, and accessible introduction to probability and statistics. This one-of-a-kind book delves into practical topics that are crucial in the analysis of sample surveys and experimentation.

Preface	p. xv
Probability and Sample Spaces	p. 1
Why Study Probability?	p. 1
Probability	p. 2
Sample Spaces	p. 2
Some Properties of Probabilities	p. 8
Finding Probabilities of Events	p. 11
Conclusions	p. 16
Explorations	p. 16
Permutations and Combinations: Choosing the Best Candidate; Acceptance Sampling	p. 18
Permutations	p. 19
Counting Principle	p. 19
Permutations with Some Objects Alike	p. 20
Permuting Only Some of the Objects	p. 21
Combinations	p. 22
General Addition Theorem and Applications	p. 25
Conclusions	p. 35
Explorations	p. 35
Conditional Probability	p. 37
Introduction	p. 37
Some Notation	p. 40
Bayes' Theorem	p. 45
Conclusions	p. 46
Explorations	p. 46
Geometric Probability	p. 48
Conclusion	p. 56
Explorations	p. 57
Random Variables and Discrete Probability Distributions-Uniform, Binomial, Hypergeometric, and Geometric Distributions	p. 58
Introduction	p. 58
Discrete Uniform Distribution	p. 59
Mean and Variance of a Discrete Random Variable	p. 60
Intervals, ¿, and German Tanks	p. 61
Sums	p. 62
Binomial Probability Distribution	p. 64
Mean and Variance of the Binomial Distribution	p. 68
Sums	p. 69
Hypergeometric Distribution	p. 70
Other Properties of the Hypergeometric Distribution	p. 72
Geometric Probability Distribution	p. 72
Conclusions	p. 73
Explorations	p. 74
Seven-Game Series in Sports	p. 75
Introduction	p. 75
Seven-Game Series	p. 75
Winning the First Game	p. 78
How Long Should the Series Last?	p. 79
Conclusions	p. 81
Explorations	p. 81
Waiting Time Problems	p. 83
Waiting for the First Success	p. 83
The Mythical Island	p. 84
Waiting for the Second Success	p. 85
Waiting for the rth Success	p. 87
Mean of the Negative Binomial	p. 87
Collecting Cereal Box Prizes	p. 88
Heads Before Tails	p. 88
Waiting for Patterns	p. 90
Expected Waiting Time for HH	p. 91
Expected Waiting Time for TH	p. 93
An Unfair Game with a Fair Coin	p. 94
Three Tosses	p. 95
Who Pays for Lunch?	p. 96
Expected Number of Lunches	p. 98
Negative Hypergeometric Distribution	p. 99
Mean and Variance of the Negative Hypergeometric	p. 101
Negative Binomial Approximation	p. 103
The Meaning of the Mean	p. 104
First Occurrences	p. 104
Waiting Time for c Special Items to Occur	p. 104
Estimating k	p. 105
Conclusions	p. 106
Explorations	p. 106
Continuous Probability Distributions: Sums, the Normal Distribution, and the Central Limit Theorem; Bivariate Random Variables	p. 108
Uniform Random Variable	p. 109
Sums	p. 111
A Fact About Means	p. 111
Normal Probability Distribution	p. 113
Facts About Normal Curves	p. 114
Bivariate Random Variables	p. 115
Variance	p. 119
Central Limit Theorem: Sums	p. 121
Central Limit Theorem: Means	p. 123
Central Limit Theorem	p. 124
Expected Values and Bivariate Random Variables	p. 124
Means and Variances of Means	p. 124
A Note on the Uniform Distribution	p. 126
Conclusions	p. 128
Explorations	p. 129
Statistical Inference I	p. 130
Estimation	p. 131
Confidence Intervals	p. 131
Hypothesis Testing	p. 133
ß and the Power of a Test	p. 137
p-Value for a Test	p. 139
Conclusions	p. 140
Explorations	p. 140
Statistical Inference II: Continuous Probability Distributions II-Comparing Two Samples	p. 141
The Chi-Squared Distribution	p. 141
Statistical Inference on the Variance	p. 144
Student t Distribution	p. 146
Testing the Ratio of Variances: The F Distribution	p. 148
Tests on Means from Two Samples	p. 150
Conclusions	p. 154
Explorations	p. 154
Statistical Process Control	p. 155
Control Charts	p. 155
Estimating ¿ Using the Sample Standard Deviations	p. 157
Estimating ¿ Using the Sample Ranges	p. 159
Control Charts for Attributes	p. 161
np Control Chart	p. 161
p Chart	p. 163
Some Characteristics of Control Charts	p. 164
Some Additional Tests for Control Charts	p. 165
Conclusions	p. 168
Explorations	p. 168
Nonparametric Methods	p. 170
Introduction	p. 170
The Rank Sum Test	p. 170
Order Statistics	p. 173
Median	p. 174
Maximum	p. 176
Runs	p. 180
Some Theory of Runs	p. 182
Conclusions	p. 186
Explorations	p. 187
Least Squares, Medians, and the Indy 500	p. 188
Introduction	p. 188
Least Squares	p. 191
Principle of Least Squares	p. 191
Influential Observations	p. 193
The Indy 500	p. 195
A Test for Linearity: The Analysis of Variance	p. 197
A Caution	p. 201
Nonlinear Models	p. 201
The Median-Median Line	p. 202
When Are the Lines Identical?	p. 205
Determining the Median-Median Line	p. 207
Analysis for Years 1911-1969	p. 209
Conclusions	p. 210
Explorations	p. 210
Sampling	p. 211
Simple Random Sampling	p. 212
Stratification	p. 214
Proportional Allocation	p. 215
Optimal Allocation	p. 217
Some Practical Considerations	p. 219
Strata	p. 221
Conclusions	p. 221
Explorations	p. 221
Design of Experiments	p. 223
Yates Algorithm	p. 230
Randomization and Some Notation	p. 231
Confounding	p. 233
Multiple Observations	p. 234
Design Models and Multiple Regression Models	p. 235
Testing the Effects for Significance	p. 235
Conclusions	p. 238
Explorations	p. 238
Recursions and Probability	p. 240
Introduction	p. 240
Conclusions	p. 250
Explorations	p. 250
Generating Functions and the Central Limit Theorem	p. 251
Means and Variances	p. 253
A Normal Approximation	p. 254
Conclusions	p. 255
Explorations	p. 255
Bibliography	p. 257
Where to Learn More	p. 257
Index	p. 259
Table of Contents provided by Ingram. All Rights Reserved.

Amazon no longer offers textbook rentals. We do!

A Probability and Statistics Companion

A Probability and Statistics Companion

9780470471951

0470471956

Summary

Author Biography

Table of Contents

Supplemental Materials

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