Instructor

* wperkins3@math.gatech.edu*

Office: Skiles 017

Office Hours: Wednesday 10 am - 12pm, or by appointment

Topics

- Sections: 2.2, 3.8, 4.8, 5.10, 5.11, 7.4, 7.5, 7.6
- Definitions:
- Weak Law of Large Numbers
- Strong Law of Large Numbers
- Central Limit Theorem
- Chernoff Bound
- Know proofs of all of the above
- Law of the Iterated Logarithm

- Theorems:
- Sample Questions:
- Prove the Central Limit Theorem
- Prove the WLLN assuming a 2nd moment
- Prove the SLLN assuming a 4th moment
- Prove a Chernoff Bound for a sum of iid Normal rv's
- Prove a Chernoff Bound for a sum of Bernoulli rv's
- If X_i has a finite variance, can the conclusion of the SLLN be strengthened at all?
- Give an example of a distribution that does not satisfy the WLLN
- Let X_i's be iid with finite mean and variance. What can you say about (X_1 + ... + X_n)/ n^{2/3} ?
- Say X_i's are iid with mean 0 and Ee^{\lambda X_i} < e^{\lambda + \lambda^2}. What can you say about Pr[(X_1 + .. X_n) >t]?
- Prove the WLLN assuming only a finite first moment
- Let Y_k have a Poisson (k) distribution. Show that as n -> \infty, a propoerly scaled Y_n converges to a Normal distribution.