Let [math]X[/math] be a continuous random variable with values in [math][\,0,1][/math], uniform density function [math]f_X(x) \equiv 1[/math] and moment generating function [math]g(t) = (e^t - 1)/t[/math]. Find in terms of [math]g(t)[/math] the moment generating function for

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