1 Some Motivating Examples -- ch. 2 Some Fundamental Concepts -- 2.1.Some Fundamental Concepts -- 2.2.Some Fundamental Results -- 2.3.Random Variables -- 2.4.Basic Concepts and Results in Counting -- ch. 3 The Concept of Probability and Basic Results -- 3.1.Definition of Probability -- 3.2.Some Basic Properties and Results -- 3.3.Distribution of a Random Variable -- ch. 4 Conditional Probability and Independence -- 4.1.Conditional Probability and Related Results -- 4.2.Independent Events and Related Results -- ch. 5 Numerical Characteristics of a Random Variable -- 5.1.Expectation, Variance, and Moment-Generating Function of a Random Variable -- 5.2.Some Probability Inequalities -- 5.3.Median and Mode of a Random Variable -- ch. 6 Some Special Distributions -- 6.1.Some Special Discrete Distributions -- 6.1.1.Binomial Distribution -- 6.1.2.Geometric Distribution -- 6.1.3.Poisson Distribution -- 6.1.4.Hypergeometric Distribution -- 6.2.Some Special Continuous Distributions -- 6.2.1.Gamma Distribution -- 6.2.2.Negative Exponential Distribution -- 6.2.3.Chi-Square Distribution -- 6.2.4.Normal Distribution -- 6.2.5.Uniform (or Rectangular) Distribution -- 6.2.6.The basics of the Central Limit Theorem (CLT) -- ch. 7 Joint Probability Density Function of Two Random Variables and Related Quantities -- 7.1.Joint d.f. and Joint p.d.f. of Two Random Variables -- 7.2.Marginal and Conditional p.d.f.'s, Conditional Expectation and Variance -- ch. 8Joint Moment-Generating Function, Covariance, and Correlation Coefficient of Two Random Variables -- 8.1.The Joint m.g.f. of Two Random Variables -- 8.2.Covariance and Correlation Coefficient of Two Random Variables -- 8.3.Proof of Theorem 1, Some Further Results -- ch. 9 Some Generalizations to k Random Variables, and Three Multivariate Distributions -- 9.1.Joint Distribution of k Random Variables and Related Quantities -- 9.2.Multinomial Distribution -- 9.3.Bivariate Normal Distribution -- 9.4.Multivariate Normal Distribution -- ch. 10 Independence of Random Variables and Some Applications -- 10.1.Independence of Random Variables and Criteria of Independence -- 10.2.The Reproductive Property of Certain Distributions -- 10.3.Distribution of the Sample Variance under Normality -- ch. 11 Transformation of Random Variables -- 11.1.Transforming a Single Random Variable -- 11.2.Transforming Two or More Random Variables --11.3.Linear Transformations -- 11.4.The Probability Integral Transform -- 11.5.Order Statistics -- ch. 12 Two Modes of Convergence, the Weak Law of Large Numbers, the Central Limit Theorem, and Further Results --12.1.Convergence in Distribution and in Probability -- 12.2.The Weak Law of Large Numbers and the Central Limit Theorem -- 12.2.1.Applications of the WLLN -- 12.2.2.Applications of the CLT -- 12.2.3.The Continuity Correction -- 12.3.Further Limit Theorems -- ch. 13 An Overview of Statistical Inference -- 13.1.The Basics of Point Estimation -- 13.2.The Basics of Interval Estimation -- 13.3.The Basics of Testing Hypotheses -- 13.4.The Basics of Regression Analysis -- 13.5.The Basics of Analysis of Variance -- 13.6.The Basics of Nonparametric Inference.