Let X₁, X₂, . . . be a sequence of i.i.d. random variables with common mean µ and MGF Mₓ.
We assume that Mₓ(s) is finite when s ∈ (−d, d) for some d > 0. Let
Xₙ := x₁ + ... + Xₙ / n

Suppose that the transform Mₓ(s) has a first-order Taylor series expansion around s = 0
of the form
Mₓₙ(s) = a + bs + o(s)