Table Of Contents
VOL. I PROBABILITY THEORY
Descriptive Statistics
Lesson 1 Frequency Distributions 1
Lesson 2 Averages 18
Lesson 3 Measuring Variation 33
Set Theory
Lesson 4 Basic Concepts 47
Lesson 5 Set Operations 52
Lesson 6 Venn Diagrams 77
Lesson 7 Cardinality of a Set 90
Lesson 8 Sample Spaces & Events 107
Lesson 9 Boolean Algebra of Sets 117
Probability Theory
Lesson 10 Probability Sample Space 137
Lesson 11 Sampling Methods 158
Lesson 12 Conditional Probability 171
Lesson 13 Bayes Theorem 213
Lesson 14 Random Variables 229
Lesson 15 Expectation of a Random Variable 256
Lesson 16 Variance of a Random Variable 270
Lesson 17 Factorials & Counting Samples 279
Lesson 18 The Binomial Sample Space 300
Lesson 19 The Binomial Random Variable 312
Lesson 20 The Binomial Distribution 319
Lesson 21 The Binomial Distribution Table 334
Lesson 22 The Poisson Distribution 346
Lesson 23 The Poisson Distribution Table 361
Lesson 24 The Poisson Approximation to the Binomial Distribution 368
Lesson 25 The Normal Distribution 373
Lesson 26 Applications Using The Normal Distribution 394
Lesson 27 The Normal Approximation To The Binomial Distribution 418
VOL. II STATISTICS
Statistics & Inference Theory
Lesson 28 The Central Limit Theorem 435
Lesson 29 Estimating the Mean of a Population 446
Lesson 30 Statistical Hypotheses 458
Lesson 31 Hypothesis Testing 463
Lesson 32 Type I Error 478
Lesson 33 Type II Error 500
Lesson 34 Combining Type I and Type II Errors 524
Lesson 35 The Distribution of 538
Lesson 36 Estimating The Proportion p of a Population 550
Lesson 37 Decision Theory Using 560
Lesson 38 The Distribution of Differences of Sample Means 572
Lesson 39 The Distribution of Differences of Sample Proportions 593
Lesson 40 Small Sampling Theory 616
Lesson 41 The F Distribution 629
Lesson 42 Analysis of Variance 635
Lesson 43 The Chi-Square Distribution 656
Lesson 44 Correlation and Regression Analysis I 688
Lesson 45 Correlation and Regression Analysis II 706
Lesson 46 Non parametric Statistics 717
Appendix A Review of the Normal Distribution 768
Tables Tables A-F 790
Complete solutions to all unsolved problems and supplementary problems are in the web site: http://www.pathwaystoclearlearning.com/
Note: Lessons in bold are linked to their respective lessons.
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