1. 5.6 The Central Limit Theorem
There are many cases for which we know the cdf and density of the sum (i.i.d.)
For example the Bernoulli, binomial, Poisson, gamma, and Gaussian.

2. Preliminary Observations
If m ≠ 0, nm → + or – ∞.

3. So, we might consider instead

6. Xi ∼ exp(1) RVs implies Yn ∼ Erlang(n,1)

9. Derivation of the CLT

18. Chapter 7 Bivariate RVs

21. Marginal Probabilities

22. Marginal Probabilities

23. Marginal Probabilities

24. Marginal Probabilities

25. Marginal Probabilities
Similarly,

32. 7.2 Jointly Continuous RVs

37. Joint and Marginal Densities

42. Conversely, if