Chapter 3: Joint Distributions

Joint Probability

Probability of two random variables occurring together.

Bivariate Function

Function representing joint distribution of two variables.

Joint Probability Mass Function

Function defining probabilities for discrete variables.

Marginal Distribution

Distribution of a subset of variables.

Joint Density Function

Function defining probabilities for continuous variables.

Copula Function

Links marginal distributions in joint distribution.

Marginal Density Function

Density function for a single variable.

Multinomial Distribution

Distribution for outcomes of multiple categories.

Conditional Probability

Probability of one event given another event.

Independence of Variables

Variables do not influence each other's probabilities.

Cumulative Distribution Function

Function giving probability that variable is less than or equal.

Jacobian

Determinant used in variable transformation.

Order Statistics

Statistics based on the ordered values of a sample.

Fréchet-Hoeffding Boundaries

Bounds for joint distributions based on marginals.

Uniform Joint Density

Density function where all outcomes are equally likely.

Transformations of Variables

Changing variables to simplify joint distributions.

Exponential Distribution

Distribution describing time until an event occurs.

Probability Mass Function (PMF)

Function giving probabilities for discrete outcomes.

Probability Density Function (PDF)

Function giving probabilities for continuous outcomes.

Marginal Probability Distribution

Probability distribution of a single variable.

Joint Distribution Function

Function defining the probability of multiple variables.

Cumulative Distribution Function (CDF)

Probability that a random variable is less than or equal.