6  Random Variables

6.1 Random Experiments

6.2 Probability

6.3 Independence

6.4 Random Variables

6.4.1 Discrete RV

6.4.1.1 Probability Mass Functions

6.4.1.2 Expectation

6.4.1.3 Variance

6.4.1.4 Moment-Generating Functions

6.4.2 Continuous RV

6.4.2.1 Probability Density Functions

6.4.2.2 Expectation

6.4.2.3 Variance

6.4.2.4 Moment-Generating Functions

6.5 Joint Distributions

6.5.1 Joint Probability Density Function

6.5.2 Conditional Density Functions

6.5.3 Marginal Density Functions

6.5.4 Independence and Covariance

6.6 Functions of Random Variables

6.6.1 Method of Distribution Functions

6.6.2 Method of Transformations

6.6.3 Method of Moment-Generating Functions