Let 1 , 2 , ... be i.i.d. r.v.s with a m.g.f. M(z), and S

Let ξ₁, ξ₂, ... be i.i.d. r.v.’s with a m.g.f. M(z), and S_t = ξ₁ + ... + ξ_t. Show that X_t = M^−t (z)exp{zS_t} is a martingale with respect to ξ_t.