Let \(X\) have the moment generating function \(M_{X}(t)\). Show that

(a) \(M_{(X+a)}(t)=e^{a t} M_{X}(t)\).

(b) \(M_{b X}(t)=M_{X}(b t)\).

(c) \(M_{(X+a) / b}(t)=e^{(a /

b) t} M_{X}(t / b)\).