Further Topics in Probability, Spring 2018
| Márton Balázs | ||
| Email: | m.balazs@our_city.ac.countrycode | |
| Tel: | +44 (0)117 928-7991 | |
| Office: | Maths 3.7 | |
| Drop in Sessions: | Tuesdays 13:00 - 14:00 on teaching weeks, Maths 3.7 | |
| Q&A Session: | Friday 25th May, 14:00, SM4. Please 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 23 Jan | Review of the unit, basic discrete distributions | -- |
| Thu 25 Jan | Basic discrete distributions; convolution (discrete cases) | -- |
| Fri 26 Jan | Ex. class (Neg.Bin convolution, continuous r.v., Normal distribution) | -- |
| Tue 30 Jan | Convolution (Gaussian) | -- |
| Thu 1 Feb | Convolution (Cauchy) | -- |
| Fri 2 Feb | Convolution (Cauchy) | HW1 (sol. on Bb.) |
| Tue 6 Feb | Gamma, Chi square distributions | -- |
| Thu 8 Feb | Poisson process. Generating functions (properties) | -- |
| Fri 9 Feb | Ex. class (convolutions) | -- |
| Tue 13 Feb | Generating functions (random no. of summands) | -- |
| Thu 15 Feb | Generating functions (Galton-Watson process) | -- |
| Fri 16 Feb | Generating functions (Critical G-W process; random walk) | HW2 (sol. on Bb.) |
| Tue 20 Feb | Generating functions (random walk: level 1 hitting time) | -- |
| Thu 22 Feb | Generating functions (weak convergence) | -- |
| Fri 23 Feb | Ex. class (fun with generating functions) | -- |
| Tue 27 Feb | Weak convergence examples, Weak Law of Large Numbers | -- |
| Thu 1 Mar | Weak Law of Large Numbers, Stirling's formula -- Cancelled | -- |
| Fri 2 Mar | Stirling's formula, DeMoivre Laplace CLT -- Cancelled | HW3 -- Due: 5th (sol. on Bb.) |
| Tue 6 Mar | Weak Law of Large Numbers, Stirling's formula | -- |
| Thu 8 Mar | Weierstrass' Approximation Thm, DeMoivre Laplace CLT | -- |
| Thu 8 Mar | DeMoivre Laplace CLT | -- |
| Fri 9 Mar | Ex. class (Generating functions: RW probabilities) | -- |
| Tue 13 Mar | Measure Theory (basic notions, probability) | -- |
| Tue 13 Mar | Measure Theory | -- |
| Thu 15 Mar | Probabilistic tools | -- |
| Fri 16 Mar | Probabilistic inequalities | HW4 (sol. on Bb.) |
| Tue 20 Mar | Convergences | -- |
| Thu 22 Mar | Strong Law of Large Numbers (Kolmogorov's ineq., Kolmogorov-Khinchin) | -- |
| Fri 23 Mar | Ex. class (convergence types) | -- |
| Easter vacation | ||
| Tue 17 Apr | Toeplitz, Kronecker; Kolmogorov's Thm, SLLN | -- |
| Thu 19 Apr | SLLN; characteristic Functions | -- |
| Fri 20 Apr | Characteristic Functions | HW5 (sol. on Bb.) |
| Tue 24 Apr | Inversion formula | -- |
| Thu 26 Apr | Inversion formula, weak convergence (Prokhorov's Thm) | -- |
| Fri 27 Apr | Ex. class (Characteristic functions) | -- |
| Tue 1 May | Weak Convergence (Prokhorov's Thm) | -- |
| Thu 3 May | Weak Convergence (Continuity Lemma) | -- |
| Fri 4 May | WLLN, CLT, comments | 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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