1 Introduction 2 Probability 2.1 Sample Space 2.2 Events 2.3 Probability of Events 2.4 Laws of Probability 2.5 Conditional Probability 2.6 Bayes' Rule Exercises 2 3 Random Variables 3.1 Definition of Random Variables 3.2 Discrete Random Variables 3.3 Expectation and Variance 3.4 Binomial Distribution 3.5 Poisson Distribution Exercises 3 4 Continuous Random Variables 4.1 Continuous Random Variables 4.2 Uniform Distribution 4.3 Normal Distribution 4.4 Normal Approximation to the Binomial Distribution 4.5 Exponential Distribution 4.6 Function of Random Variables 4.7 Chebyshev's Theorem Exercises 4 5 Random Vectors and Joint Probability Distributions 5.1 Concept of Joint Probability Distributions 5.2 Conditional Distribution 5.3 Statistical Independent 5.4 Covariance and Correlation 5.5 Law of Large Numbers and Central Limit Theorem Exercises 5 6 Fundamental Sampling Distributions and Data Descriptions 6.1 Analysis of Data 6.2 Random Sampling 6.3 Statistics 6.4 Sample Distributions 6.5 Chi-square Distribution 6.6 Student's Distribution (t-Distribution) 6.7 F-Distribution Exercises 6 7 Estimation Problems 7.1 Point Estimation 7.2 Interval Estimation 7.3 Determination of the Sample Size 7.4 Maximum Likelihood Estimation Exercises 7 8 Testing Hypothesis 8.1 Statistical Hypothesis:General Concepts 8.2 Testing a Statistical Hypothesis
8.3 Hypothesis Concerning Mean 8.4 Hypothesis Concerning Variance 8.5 Relationship to Confidence Interval Estimation 8.6 Tests for Proportion 8.7 Tests for Independence 8.8 Goodness-of-Fit Test Exercises 8 9 Nonparametric Statistics 9.1 Sign Test 9.2 Rank-Sum Test 9.3 Signed-Rank Test Exercises 9 10 Regression and Correlation 10.1 Introduction 10.2 Simple Linear Regression Equation 10.3 Parameter Estimation 10.4 Tests the Usefulness of the Linear Regression Model 10.5 Predictions 10.6 Multiple Linear Regression 10.7 Linearizable Models 10.8 Normal Correlation Model Exercises 10 11 Analysis of Variance 11.1 Introduction 11.2 One-Way Analysis of Variance 11.3 Two-Way Analysis of Variance Exercises 11 Answer to Exercises Review Exercises Appendix References
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