Further Topics in Probability, Spring 2017
| Márton Balázs | ||
| Email: | m.balazs@our_city.ac.countrycode | |
| Tel: | +44 (0)117 928-7991 | |
| Office: | Maths 3.7 | |
| Drop in Sessions: | Tuesdays 17:00 - 18:00 on teaching weeks, Maths 3.7 | |
| Q&A Session: | Friday 19th May, 14:00, SM2. Prepare with questions. |
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Below is a detailed schedule. Topics of future events are plans, and can change. Topics of past events serve as log.
Homeworks are/will also be posted here: just click those with a link below. They are due in class, or in the blue locker with my name on the ground floor of the Main Maths Building.
Homework solutions will appear on Blackboard, please email me if you have problem accessing these.
I was thinking about going over the ingenious proof of the SLLN by N. Etemadi, but decided to stay with the classical way instead. You are welcome to check out his way of doing it!
Came across this illustration of Jensen's inequality: square-root of the average ≠ average of the square-root.
| Day | Topics | Homework due: |
|---|---|---|
| Tue 24 Jan | Review of the unit, basic discrete distributions | -- |
| Wed 25 Jan | Convolution (discrete cases) | -- |
| Thu 26 Jan | Ex. class (Neg.Bin convolution, continuous r.v., Normal distribution) | -- |
| Tue 31 Jan | Convolution (Gaussian) | -- |
| Wed 1 Feb | Convolution (Cauchy) | -- |
| Thu 2 Feb | Convolution (Cauchy, Exponential) | HW1 (sol. on Bb.) |
| Tue 7 Feb | Gamma, Chi square distributions | -- |
| Wed 8 Feb | Poisson process. Generating functions (properties) | -- |
| Thu 9 Feb | Ex. class (convolutions) | -- |
| Tue 14 Feb | Generating functions (random no. of summands) | -- |
| Wed 15 Feb | Generating functions (Galton-Watson process) | -- |
| Thu 16 Feb | Generating functions (Critical G-W process; random walk: level 1 hitting time) | HW2 (sol. on Bb.) |
| Tue 21 Feb | Generating functions (random walk) | -- |
| Wed 22 Feb | Generating functions (Weak convergence, Poisson approximation) | -- |
| Thu 23 Feb | Ex. class (fun with generating functions) | -- |
| Tue 28 Feb | Weak convergence examples, Weak Law of Large Numbers | -- |
| Wed 1 Mar | Weak Law of Large Numbers, Stirling's formula | -- |
| Thu 2 Mar | Stirling's formula, DeMoivre Laplace CLT | HW3 (sol. on Bb.) |
| Tue 7 Mar | DeMoivre Laplace CLT | -- |
| Wed 8 Mar | Measure Theory (basic notions, probability) | -- |
| Thu 9 Mar | Ex. class (Generating functions: RW probabilities) | -- |
| Tue 14 Mar | Measure Theory | -- |
| Wed 15 Mar | Probabilistic tools | -- |
| Thu 16 Mar | Probabilistic inequalities | HW4 (sol. on Bb.) |
| Tue 21 Mar | Convergences | -- |
| Wed 22 Mar | Strong Law of Large Numbers (Kolmogorov's ineq., Kolmogorov-Khinchin) | -- |
| Thu 23 Mar | Toeplitz, Kronecker; Kolmogorov's Thm, SLLN | -- |
| Tue 28 Mar | Ex. class (convergence types) | -- |
| Wed 29 Mar | SLLN; characteristic Functions | -- |
| Thu 30 Mar | Characteristic Functions (Inversion formula) | -- |
| Easter vacation | ||
| Tue 25 Apr | Inversion formula and its consequences | HW5 (sol. on Bb.) |
| Wed 26 Apr | Weak Convergence, CLT (Prokhorov's Thm) | -- |
| Thu 27 Apr | Ex. class (Characteristic functions) | -- |
| Tue 2 May | Weak Convergence, CLT (Continuity Lemma) | -- |
| Wed 3 May | Weak Convergence, WLLN, CLT | -- |
| Thu 4 May | Comments on the CLT (Berry-Esséen, Local CLT, Lindeberg Thm) | HW6 (sol. on Bb.) |
If you have any questions, please contact me (see on top). Click here to see my schedule.
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