Further Topics in Probability, Spring 2018
Márton Balázs  
Email:  m.balazs@our_city.ac.countrycode  
Tel:  +44 (0)117 9287991  
Office:  Maths 3.7  
Drop in Sessions:  Tuesdays 13:00  14:00 on teaching weeks, Maths 3.7  
Q&A Session:  Friday 25^{th} May, 14:00, SM4. Please prepare with questions. 

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: squareroot of the average ≠ average of the squareroot.
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 (GaltonWatson process)   
Fri 16 Feb  Generating functions (Critical GW 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: 5^{th} (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., KolmogorovKhinchin)   
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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