5 Properties of a Random Sample

5.1 Basic Concepts of Random Samples

5.2 Sums of Random Variables from a Random Sample

5.3 Sampling from the Normal Distribution

5.3.1 Properties of the Sample Mean and Variance

5.3.2 The Derived Distributions: Student’s t and Snedecor’s F

5.4 Order Statistics

5.5 Convergence Concepts

5.5.1 Convergence in Probability

5.5.2 Almost Sure Convergence

5.5.3 Convergence in Distribution

5.5.4 The Delta Method

5.6 Generating a Random Sample

5.6.1 Direct Methods

5.6.2 Indirect Methods

5.6.3 The Accept/Reject Algorithm

5.7 Miscellance