Further Topics in Probability, Spring 2017
Márton Balázs  
Email:  m.balazs@our_city.ac.countrycode  
Tel:  +44 (0)117 9287991  
Office:  Maths 3.7  
Drop in Sessions:  Tuesdays 17:00  18:00 on teaching weeks, Maths 3.7  
Q&A Session:  Friday 19^{th} May, 14:00, SM2. 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 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 (GaltonWatson process)   
Thu 16 Feb  Generating functions (Critical GW 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., KolmogorovKhinchin)   
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 (BerryEsséen, 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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