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0 Introduction 0.1 Introduction to Probability 0.2 Introduction to Statistics 1 Probability of Events 1.1 Experiments and Events 1.2 Set Theory 1.3 Frequency and Probability 1.4 The Classical Probability 1.5 Geometrical Probability 1.6 Conditional Probability 1.7 Independence of Events Exercises 1 2 Random Variables and Distributions 2.1 Random Variables and Distribution Functions 2.2 Discrete Random Variables 2.3 Continuous Random Variables 2.4 Functions of a Random Variable Exercises 2 3 Multivariate Random Variables 3.1 Bivariate Random Variables 3.2 Marginal Distributions 3.3 Conditional Distributions 3.4 Independent Random Variables 3.5 Functions of Two or More Random Variables 3.6 Multivariate Distributions Exercises 3 4 Numerical Characteristics of Random Variables 4.1 Mathematical Expectation 4.2 Variance 4.3 Covariance and Correlation Coefficient 4.4 Moments Exercises 4 5 Law of Large Numbers and Central Limit Theorem 5.1 Law of Large Numbers 5.2 Central Limit Theorem Exercises 5 6 Random Samples and Sampling Distributions 6.1 Random Samples 6.2 Sampling Distributions Exercises 6 7 Parametric Estimation 7.1 Point Estimation 7.2 Evaluation of Estimators 7.3 Interval Estimation 7.4 One-sided Confidence Interval Exercises 7 8 Testing Hypotheses 8.1 Problems of Testing Hypotheses 8.2 Testing Hypotheses about Normal Distribution 8.3 P-value Exercises 8 9 Linear Regression Analysis 9.1 Simple Linear Regression Analysis 9.2 Linearizable Nonlinear Regression 9.3 Multiple Linear Regression Exercise 9 10 Analysis of Variance 10.1 Single-Factor Analysis of Variance 10.2 Variance Analysis of Two-Factor Equal Repeated Experiments 10.3 Variance Analysis of Two-Factor Non-Repeated Experiments Exercises 10 Appendix 1 Table of Binomial Distribution Appendix 2 Table of Poisson Distribution Appendix 3 Table of Standard Normal Distribution Appendix 4 Table of the t Distribution Appendix 5 Table of the x2 Distribution Appendix 6 Table of the F Distribution Appendix 7 One-sided P-values from t Distribution: P(t(n)£¾t) Appendix 8 Key to Exercises References