STAT 414, section 002: Introduction to Probability Theory
NOTE: The homework assignment for each week is due at the beginning of class on
Thursday the following week.
For example, homework from Chapter 1 is due on January 17th.
| Week | Sections | Homework Assignment (Note: due date is always the following week!) |
| Jan. 7-11 | Basic combinatorics: 1.1-1.5 | 1-33; Theor. 8, 10, 12 |
| Jan. 14-18 | Axioms of probability, sample spaces: 2.1-2.5 | 4, 10, 12, 18, 23, 27, 36, 39; Theor. 10, 11, 12 |
| Jan. 21-25 | Conditional probability, Bayes' theorem: 3.1-3.3 | 2, 5, 6, 11, 12, 15, 18, 21, 23, 28 |
| Jan. 28-Feb. 1 | Independent events, more on conditional probability: 3.3-3.5 | 37, 39, 43, 50, 52, 55, 64, 65, 78; Theor. 1, 6 |
| Feb. 4-8 | Random variables, discrete r.v.s, expectations: 4.1-4.3 | 1, 5, 7, 13, 17, 20, 21, 25; Theor. 1, 10 |
| Feb. 11-15 | Expectations, variance, Bernoulli and Binomials r.v.s: 4.4-4.6 | 30, 35, 38, 41, 42, 46, 49; Theor. 14 |
| Week of Feb. 11th | Mid-term Exam 1 | In class. |
| Feb. 18-22 | Poisson, Geometric, Negative Binomial, Hypergeometric, others; expected values of sums: 4.7-4.9 | 51, 53, 54, 59, 61, 77, 78, 79; Theor. 16, 17 |
| Feb. 25-Mar. 1 | Continuous r.v.s, Uniform, Normal distributions: 5.1-5.4 | 2, 3, 5, 6, 8, 10, 13, 15, 16; Theor. 1, 7; Extra credit: 63, 65, 80 (pp. 177-179) |
| Mar. 11-15 | Exponential, other continous (e.g. Gamma, Weibull etc.); transformations: 5.4-5.7 | 19, 21, 23, 27, 31, 33, 35; Theor. 9, 13 |
| Mar. 18-22 | Joint distributions; independence, sums of independent r.v.s; conditional pmfs: 6.1-6.2 | 1, 3, 9, 10, 15, 20, 21, 23; Theor. 9 HW 10 is due April 4th. |
| Mar. 25-29 | Exam review and midterm exam | New item: no HW due during the week of Midterm 2. |
| Week of March 25 (Thursday) | Mid-term Exam 2 | In class. |
| Apr. 1-5 | conditional pdfs, pmfs; order statistics; multivariate transformations: 6.3-6.7 | 26, 27, 29, 30, 31, 36, 41, 42, 55; Theor. 11 HW 11 is due April 11th. |
| Apr. 8-12 | Expectations of sums; covariances: 7.1-7.4 | 1, 3, 6, 16, 18, 21, 26; Theor. 1, 2 HW 12 is due April 18th. |
| Apr. 15-19 | conditional expectations, law of iterated expectations, joint mgfs: 7.5-7.7 | 33, 36, 39, 41, 51, 55, 56, 68; Theor. 4 HW 13 is due April 25th. |
| Apr. 22-26 | Limit theorems, Chebyshev's; Weak Law of Large Numbers; Central Limit Theorem;Strong Law of Large Numbers; Inequalities: 8.1-8.5 | 1, 4, 5, 7, 8, 13, 15, 18, 19; Theor. 7 (Hint: logarithms) HW 14 is due no later then at final exam time, 4/30/2013. You may turn it in early in my office. Extra credit: You may solve one of the following problems: 20, 22, 23. |
| April 29-May 3 | Comprehensive Final Exam | Tuesday 30 April 2013. Location TBD. |