Let [math]X[/math] be a discrete random variable with values in [math]\{0,1,2,\ldots,n\}[/math] and moment generating function [math]g(t)[/math]. Find, in terms of [math]g(t)[/math], the generating functions for

• [math]-X[/math].
• [math]X + 1[/math].
• [math]3X[/math].
• [math]aX + b[/math].