Chapter 1 Preliminaries

This first chapter contains a probability review and the required machinery for subsequent chapters. Particularly relevant are random vectors and their transformations, and the moment generating function.

$The pdf of $X\sim\mathcal{N}(\mu,1)$ (solid lines) and the pdf of $Y=X^2$ (dashed lines), for a range of values of $\mu$.$

Figure 1.1: The pdf of $X\sim\mathcal{N}(\mu,1)$ (solid lines) and the pdf of $Y=X^2$ (dashed lines), for a range of values of $\mu$ .