Week starting  Monday  Wednesday  Friday  Homework  topic planned  notes  

4 Sept  Ex 1, Ex 2  Ex 3; Ex 4 up to state diagram  Probability rules. 
Chap 1, Ex 16  
11 Sept  Ex 4 up to 5/12 soln; Ex 5  Ex 6 (briefly); Ex 9 A  (E5) and Ex 9B; Ex 8; heuristics for Ex 10  #1 due 13 Sept  Conditioning. Start expectations.  
18 Sept  Ex 10; Ex 11;  final symmetry argument for Ex 11; Ex 12.  Ex 13, with discussion of (E5)  #2 due 20 Sept  (conditional) expectations.  Chap 2 Ex 714  
25 Sept  Ex 15, 16, 17.  Ex 18; state Ex 20.  Ex 20; discussion of ways to find symmetry  #3 due 27 Sept  Binomial distribution. Start symmetry.  Chap 3 Ex 1519  
2 Oct  Explanation for Ex 21; start variances  Ex 23 (only first part); Ex 24; Ex 25.  Ex 26; sketch of Ex 27  #4 due 4 Oct  Symmetry, sampling, variances, covariances. 
Chap 4
Ex2022 Chap 5 Ex2327 

9 Oct  Ex 28  Ex 29  Ex 30, 31,32  #5 due 11 Oct  Continuous distributions and densities.  Chap 6 Ex 2832  
16 Oct  Ex 33, 34  Ex 35, 36  MIDTERM test (in class) 
#6 due 18 Oct  Normal distributions and CLT.  Chap 7 Ex 3338 Appendix  
23 Oct  Ex 37, 38  Ex 39, 40  Ex 41; start Poisson proc 
no homework due this week  Poisson approximation and Poisson processes. 
Chap 8 Ex 3941 

30 Oct  Ex 42; std exp; indep times between points 
Ex 43, 44  Ex 45, 46  #7 due 1 Nov  Gamma and other distributions derived from Poisson processes. 
Chap 9 Ex 4246 

6 Nov  Ex 47; start Ex 48  finish Ex 48; mention Ex 49; start Ex 50  finish Ex 50; 51  #8 due 8 Nov  Bivariate densities. Jacobians by first principles. 
Chap 10 Ex 4751 

13 Nov  DP Jury duty; no lecture at Yale 
start Ex 52  finish Ex 52; Ex 53  #9 due 15 Nov  More bivariate densities: conditional densities. 
Chap 11 Ex 5253 

20 Nov  Fall recessno classes  
27 Nov  Ex 54  Ex 55, 56  Ex 57, 58  no homework due this week  Multivariate normal. 
Chap 12 Ex 5458 

4 Dec  Ex 59  Ex 60  Ex 61  #10 due 6 Dec  Brownian motion 
Chap 13 Ex 5961 

11 Dec  Friday 15 Dec FINAL EXAM 2:00 to 5:00 ML 211 
The coin tossing model will generate the standard discrete distributions Binomial, Poisson, geometric, negative binomial. The Poisson process, the continuous time analog of coin tossing, will generate the standard continuous distributions exponential and gamma.
Normal approximations and calculations related to the multivariate normal distribution will exercise the multivariable calculus skills of the class (or provide a crash course in multiple integrals).
Applications to include: Markov chains; the probability theory of games, gambling, and insurance; coding theory; queueing theory; branching processes; geometric probability and stereology; (maybe) analysis of algorithms.