Further Topics in Probability, Spring 2020
| Márton Balázs | ||
| Email: | m.balazs@our_city.ac.countrycode | |
| Offices: | 1.44 Fry | |
| BlueJeans Sessions: | Teaching weeks Wednesdays 10:00 - |
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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. The green version uses less paper to print. They are due at 12:00pm in the locker with "Further Topics in Probability" on it in G.90 Fry Building in Blackboard, click "Assessment, submission and feedback". A single pdf file (scanned or from LaTeX) is preferred, see instructions here or LaTeX resources on our Intranet → Software.
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 argument instead. You are welcome to check out his way of doing it!
I came across this illustration of Jensen's inequality: square-root of the average ≠ average of the square-root.
| Original plan | New setup: | Topics | Watch online: | Homework due: |
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| Tue 28 Jan | Review of the unit, basic discrete distributions | -- | ||
| Wed 29 Jan | Basic discrete distributions; convolution (discrete cases) | -- | ||
| Fri 31 Jan | Ex. class (Neg.Bin, Binom., Poi. convolution, continuous r.v.) | -- | ||
| Tue 4 Feb | Normal distribution, Convolution (Uniform, Gaussian) | -- | ||
| Wed 5 Feb | Convolution (Gaussian, Cauchy) | -- | ||
| Thu 6 Feb | -- | HW1 HW1 (sol. on Bb.) | ||
| Fri 7 Feb | Convolution (Cauchy) | -- | ||
| Tue 11 Feb | Gamma, Chi square distributions | -- | ||
| Wed 12 Feb | Generating functions (properties) | -- | ||
| Fri 14 Feb | Ex. class (convolutions, Poisson process) | -- | ||
| Tue 18 Feb | Generating functions (random no. of summands) | -- | ||
| Wed 19 Feb | Generating functions (Galton-Watson process) | -- | ||
| Thu 20 Feb | -- | HW2 HW2 (sol. on Bb.) | ||
| Fri 21 Feb | Generating functions (Critical G-W process; random walk) | -- | ||
| Tue 25 Feb | Generating functions (random walk: level 1 hitting time) | -- | ||
| Wed 26 Feb | Generating functions (weak convergence) | -- | ||
| Fri 28 Feb | Ex. class (fun with generating functions) | -- | ||
| Tue 3 Mar | Weak convergence examples, Weak Law of Large Numbers | -- | ||
| Wed 4 Mar | Weak Law of Large Numbers, Stirling's formula | -- | ||
| Thu 5 Mar | -- | HW3 HW3 (sol. on Bb.) | ||
| Fri 6 Mar | Stirling's formula, DeMoivre Laplace CLT | -- | ||
| Tue 10 Mar | Stirling's formula, DeMoivre Laplace CLT | -- | ||
| Wed 11 Mar | Measure Theory (basic notions, probability) | -- | ||
| Fri 13 Mar | Ex. class (Generating functions: RW probabilities (sol. on Bb)) | E1. on Bb. | -- | |
| Tue 17 Mar | Measure Theory | -- | ||
| Wed 18 Mar | A product-sum lemma, probabilistic tools | L1. L2. L3. L4. | -- | |
| Thu 19 Mar | Feel free to email this to me in pdf or picture format. | HW4 HW4 (sol. on Bb.) | ||
| Easter vacation | ||||
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Do it by Tue 21 Apr | Probabilistic tools and inequalities | L5. L6. L7. L8. L9. | -- |
| Wed 22 Apr; 10:00 | BlueJeans live meeting | -- | -- | |
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Do it by Wed 22 Apr | Modes of convergence, SLLN (Kolmogorov's ineq.) | L10. L11. L12. L13. L14. | -- |
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Do it by Fri 24 Apr | Ex. class (convergence modes) | E2. E3. E4. E5. | -- |
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Do it by Tue 28 Apr | SLLN (Kolmogorov-Khinchin; Toeplitz' lemma; Kronecker) | L15. L16. L17. | -- |
| Wed 29 Apr; 10:00 | BlueJeans live meeting | -- | -- | |
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Do it by Wed 29 Apr | SLLN (Kolmogorov's Thm, final proof, remarks) | L18. L19. L20. L21. L22. | -- |
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Thu 30 Apr; 12:00 | -- | -- | HW5 (sol. on Bb.) |
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Do it by Fri 1 May | Characteristic Functions | L23. L24. L25. L26. L27. | -- |
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Do it by Tue 5 May | Inversion formula, Weak convergence | L28. L29. L30. | -- |
| Wed 6 May; 10:00 | BlueJeans live meeting | -- | -- | |
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Do it by Wed 6 May | Weak Convergence (Prokhorov's Thm) | L31. L32. | -- |
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Do it by Fri 8 May | Ex. class (Characteristic functions) (sol. on Bb) | E6.,E7.,E8.,E9.,E10.,E11. on Bb. | -- |
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Do it by Tue 12 May | Continuity Lemma | L33. L34. L35. L36. | -- |
| Wed 13 May; 10:00 | BlueJeans live meeting | -- | -- | |
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Do it by Wed 13 May | WLLN, CLT | L37. L38. L39. | -- |
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Thu 14 May; 12:00 | -- | -- | HW6 (sol. on Bb.) |
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Do it by Fri 15 May | Comments on the CLT (Berry-Esseen, Local CLT, Lindeberg Thm) | L40. L41. L42. | -- |
If you have any questions, please contact me (see on top). Click here to see my schedule.
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