[math] \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}[/math]

Let [math]X[/math] be a random variable with density function [math]f_X[/math], and

let [math]Y = X + b[/math], [math]Z = aX[/math], and [math]W = aX + b[/math], where [math]a \ne 0[/math]. Find the density functions [math]f_Y[/math], [math]f_Z[/math], and [math]f_W[/math]. (See Exercise Exercise.)