Last updated November 23, 2009.
IMPORTANT INFORMATION: Take home test to be distributed on Nov. 24. Due Nov. 30. See below.
Day and Date  Section 
Topics 
Notes 
Homework Problems Assigned 

T 
8/25 
1.1, 1.2 
Probabilistic Experiments  Experiment, outcome, sample space event. Notes  Due 9/1. 9: 4, 6 (assume different identity for each coin), 13, 20. 
Th 
8/27 
1.3, 1.4 
Probability Axioms 
Practice problems. Rules for assigning probabilities to events  Due 9/3. 23: 5, 7, 15, 25, 26, 27. 37: 14. 
T 
9/1 
2.1, 2.2, 2.3 
Counting principles  Matching problem. (Needs Mathematica; get student verion here).  Due 9/8. 44: 8,17, 22, 27, 28. 50: 4, 5, 12, 24, 28(sol). 63: 1, 2, 3, 4, 5. 
Th 
9/3 
2.4 
Combinations  n choose r and applications. Poker hands.  Due 9/8. 65: 20 (find the probability of each kind of poker hand). 
T 
9/8 
2.4, 3.1 
Combinations (cont.), Conditional prob.  Examples.  Due 9/15. 63: 9(soln), 13, 29. 71: 3, 5, 6, 8, 21(soln). 82: 3, 4, 7, 13(soln). Some simple worked examples from Ch. 2 here. 
Th 
9/10 
3.1, 3.2, 3.3, 3.4 
Conditional prob. and related ideas  Summary of main formulae. 3.2 and trees. Bayes Theorem example (exercise 1) worked with Bayes and by 2by2 table, with marginals.  Due 9/15: 82: 9(soln), 11, 17. 87: 6, 9. 96: 8, 19(soln), (22 for bonus pts). 106: 3, 15 (solution to 15). 
T 
9/15 
3.5 
Independence  Definitions; simple examples; twobytwo tables.  Study! 
Th 
9/17 
3 
Review  Study! 

T 
9/21 
3.5 
Test  Test  
Th 
9/23 
4.1, 5.1 
Random variables; binomial distribution  Activity sheet  Finish activity sheet. 
T 
9/28 
4.4, 5.1 
binomial distribution (cont.); expectation.  Properties of binomial distribution with parameters n and p. (Mathematica notebook on binomial distriction, here.) Definition of expectation. View some neat graphics related to the binomial distribution: 
Problems on expectation: 173: 3, 6, 13. If I have n different pairs of socks in the dryer, each pair of a different color and design, and I take them out one sock at a time, how many socks should I expect to have removed when I first get a match? (Try this for n = 3, 4, 5.) ( The general answer is: (4^n)/Binomial[2 n, n].) (Also see: this blog.) 
T 
10/6 
4.5 
Variance; mean of binomial.  Proof of expectation of binomial  182: 6, 10. 186: 4, 5. 196: 6, 10, 19, 24. 
Th 
10/8 
4.5, 4.6, 5.1 
Review of basic concepts: random variable, probability mass function, expectation.  Handout.  199: 25. Problem: If you roll a single die repeatedly, how many rolls on average will it take to get a 6? If you roll repeatedly, how many rolls on average will it take to get a number strictly bigger than 4? If you roll repeatedly, how many rolls will it take on average to record all six possible numbers? 
T 
10/13 
Homework. Poisson distribution.  Graph of class data.  none assigned  
Th 
10/15 
Overview of ch 4 and 5  Concept Summary  Due 10/20. From the handout on 10/8: 41, 44, 45, 48, 55.  
T 
10/20 
6.1, 6.2 
Continuous distributions  Examples. Definitions. PDF, CDF. Finding PDF of g(X).  Due 10/27. 245: 1, 3, 5, 7. 
Th 
10/22 
6.3 
Expectation  Definition. Expressing expectation via CDF. E(g(X)). Examples (Cauchy distribution derived. When [0,1] divided at random point, what is expected length of the part containing p.)  Due 10/27. 254: 1, 3, 5, 9. 
T 
10/27 
7.1 
Uniform distribution  Find the standardization of the uniform distribution on [a, b].  
Th 
10/29 
7.2 
Normal distribution  Look at this cartoon of the binomial and the normal.  TAKE HOME TEST DUE 11/3. (Extra credit problem included.) See here. 
T 
11/03 
5.2, 7.3 
Poisson Processes and Exponential Distribution  212: 16, 19  
Th 
11/05 
7.3 (cont) 
Exponential  290: 5, 8, 11  
T 
11/10 
8.1 
Joint Distributions  326: 5, 11, 13  
Th 
11/12 
8.2 
Independence  339: 1, 3, 6, 8, 9, 13  
T 
11/17 
7.4 & 8.3 
Gamma Distr. & Conditional Distr.  Prove that Gamma(1)=1, Gamma(r+1) = r Gamma(r) (cf. p. 293), so Gamma(n+1) = n!. 296: 2, 6, 8.  
Th 
11/19 
8.3 & 8.4 
Conditional Expectation. Sums of independent variables and convolution.  Quiz. Study 212: 19, 290: 11, 296: 3.  355: 11,12, 21 
T 
11/24 
Quiz. Similar to the last problem (on normal distributions) from this old final. Also, you will receive a takehome test. 