An introduction to probability and statistics using BASIC

✍ Scribed by Groeneveld, Richard A

• Publisher: CRC Press
• Year: 2020
• Tongue: English
• Leaves: 465
• Edition: First edition
• Category: Library

✦ Synopsis

Core curriculum mathematics program based on the best teaching practices of top-performing Singapore, Republic of Korea, and Hong Kong. Developed in collaboration with the Singapore Ministry of Education, its proven approach and consistent lesson design create a powerful learning ecosystem for premier instruction.

✦ Table of Contents

Cover......Page 1
Half Title......Page 2
Series Page......Page 4
Title Page......Page 6
Copyright Page......Page 7
Dedication......Page 8
CONTENTS......Page 10
PREFACE......Page 14
LIST OF BASIC PROGRAMS......Page 18
Chapter 1. INTRODUCTION......Page 20
1.1 Probability and Statistics......Page 21
1.2 The Use of BASIC Programs......Page 22
2.1 Random Experiments......Page 24
2.2 Definition of a Probability Model in the Discrete Case......Page 27
2.3 Probabilities of Events in the Discrete Case......Page 38
2.4 Probabilities of Composite Events in a Discrete Sample Space S......Page 40
2.5 Conditional Frequency and Conditional Probability......Page 51
2.6 Independent Events......Page 57
3.1 Discrete Random Variables......Page 65
3.2 The Moments of a Discrete Random Variable......Page 71
3.3 The Binomial Random Variable......Page 83
3.4 The Hypergeometric Distribution......Page 99
3.5 The Poisson Distribution......Page 109
3.6 The Standard Deviation and the Chebyshev Inequality......Page 118
4.1 Introduction to Continuous Outcome Spaces......Page 122
4.2 Continuous Probability Measures and Random Variables......Page 131
4.3 Moments of a Continuous Random Variable......Page 138
4.4 Special Continuous Random Variables......Page 146
4.5 Transformations of Continuous Random Variables......Page 161
4.6 Generating Random Samples from Continuous Distributions......Page 167
5.1 Introduction......Page 171
5.2 Statistics Estimating Location......Page 185
5.3 Statistics Estimating Variability......Page 194
5.4 The Central Limit Theorem......Page 203
5.5 Estimation of μ Using Large Samples......Page 213
5.6 Approximation of Binomial Probabilities by the Normal Distribution......Page 220
6.1 Introduction and Definitions......Page 226
6.2 Estimation of Location in Small Samples......Page 232
6.3 Estimating σ2, the Population Variance......Page 245
6.4 Estimation of σ in a Normal Population......Page 251
6.5 Estimation of a Population Proportion p......Page 255
7.1 Introduction......Page 264
7.2 Tests of a Population Proportion p for Large n......Page 273
7.3 Tests Concerning μ in Normal Populations......Page 280
7.4 Tests for μ in Large Samples......Page 293
7.5 Distribution-free Tests of Location......Page 298
7.6 Tests Concerning σ2 and σ in Normal Populations......Page 311
8.1 Introduction......Page 315
8.2 Differences of Population Expectations in the Large Sample Case......Page 316
8.3 Differences of Population Expectations in the Normal Case......Page 323
8.4 The Wilcoxon Rank Sum Test......Page 331
8.5 Inference for Matched Pairs......Page 339
8.6 Comparison of Two Population Proportions......Page 344
9.2 The Multinomial Distribution and Its Relation to the Chi-Square Distribution......Page 350
9.3 Analysis of Contingency Tables......Page 356
9.4 Goodness of Fit......Page 366
10.1 Introduction (The Least Squares Line)......Page 372
10.2 Inference in the Linear Regression Model......Page 377
10.3 Prediction Using the Regression Model......Page 392
10.4 Association and Correlation......Page 396
11.1 Introduction......Page 411
11.2 Single-Factor Analysis of Variance......Page 412
11.3 The Randomized Block Design......Page 425
A.1 An Introduction to BASIC......Page 433
A.2 Elementary Statements and Operations in BASIC......Page 436
A.3 Additional Information about BASIC......Page 442
APPENDIX B: TABLES......Page 446
SELECTED BIBLIOGRAPHY AND REFERENCES......Page 458
SUBJECT INDEX......Page 461