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 2-by-2 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; two-by-two 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 take-home test. | |||