Generating Functions, Taylor Series, Taylor Theorem, Central Limit Theorem, Deep Dives.
by Author) To prove this statement, we’ll use the property of the MGF (see Eq. 5) that if the MGFs of X and Y are identical, then so are their CDFs. Here, it’ll be sufficient to show that as n tends to infinity, the MGF of Z_bar_n converges to the MGF of N(0, 1) which as we know (see Eq. 8) is ‘e’