D. Multivariate Distributions

Given i.i.d. data \(X_1, \dots, X_n\), we know how to determine the distributions of statistics such as

• the sample mean \(\bar X\), and more generally, functions of means \(g(\bar X)\) (Unit B), and
• order statistics \(X_{(k)}\), such as the sample median (Unit C).

A general statistic is of the form \(g(X_1, \dots, X_n)\). In this unit, we will develop tools for finding the sampling distribution of a general statistic.