The Geometry of Gaussian Vectors

In this post we will see how many of the classical test statistics \(z, t, F\) come from viewing a random sample as defining a vector in space, and understanding the geometry of these vectors.

1 - Gaussian Vector

Let \(X_1, \dots, X_n \sim N(\mu, \sigma^2)\) be independent and identically distributed random variables. Each such random sample can be viewed as a vector \((X_1, \dots, X_n) \in \mathbb{R}^n\).