1 Sums Are Normal

The Central Limit Theorem basically states that when we add a lot of random variables together, the SUM of all of them is approximately Normal. This is the reason why the Normal Distribution plays such an important role in probability and statistics. The theorem is true under a wide variety of different types of conditions. Our main concern will not be with proofs and results. Rather, we will show how this theorem provides very useful approximate solutions to a wide variety of real life problems.

S1 The Cumulant Generating Function

S2 Cumulants and Moments

S3 Properties of Cumulants

S4 Central Limit Theorem

S5 Generalizations of the CLT