Math 362, Introduction to Probability

Fall 2015

Topics, Exams and Homework Assignments

Week Dates Topics Sections Covered Homework Due
1 Aug 24—Aug 28 Probability in the World Around Us. Randomness with known and unknown structure. Introduction to R. 1.1, 1.2, 1.3, 1.4, 1.5, 2.1, 2.2 2.2: 2.5, 2.7, 2.9, 2.13
R:  R1 		Sep 2
2 Aug 31—Sep 4 Sample Spaces and Events. 2.3 2.3: 2.17, 2.19, 2.21, 2.23 Sep 9
3 Sep 7 Labor Day - no class.
R (Posted):  R2 		Sep 30
3 Sep 9—Sep 11 More on sets, sample spaces, events. Inclusion-Exclusion Principle for 2 sets and 3 sets (Example 2.2). 2.2, 2.3
Inclusion-Exclusion for 2/3 sets:  Solve Example 2.2 and practice on similar problems.		 Sep 16
4 Sep 14—Sep 18 Definition of Probability. Counting Rules Used in Probability. 2.4, 2.5 2.4: 2.35, 2.37, 2.45, 2.48, 2.51, 2.53, 2.61, 2.5: 2.67, 2.69, 2.71 Sep 21
5 Sep 21 Counting rules. Multi-stage processes. Two-way tables. Probability trees. Review for Midterm 1. 2.4, 2.5
R (Reminder):  R2 		Sep 30
5 Sep 23 TAKE-HOME MIDTERM 1 POSTED. Counting Rules. Permutations, Combinations. Distinct vs. identical items. 2.4, 2.5
5 Sep 25 Counting Rules used in Probability. Review of Take-Home Midterm 1 topics. Assignment R2.
6 Oct 6 NOTE: This syllabus item is added purely to describe R Assignment 3. The topics in this assignment cover: counting rules, conditional probability, Bayes Formula, computing contingency tables with R, computing multinomial coefficients. First encounter of the multi-nomial distribution. 2.4, 3.1, 3.2, 3.3
R (Posted):  R3 		Oct 21
6 Sep 28—Oct 3 Conditional Probability. Independence. Theorem on Total Probability and Bayes Rule. 3.1, 3.2, 3.3 3.1: 3.5, 3.13, 3.15, 3.2: 3.27, 3.35, 3.37 Oct 7
7 Oct 5—Oct 9 Theorem on Total Probability and Bayes Rule. 3.3 3.3: 3.43, 3.45, 3.48, 3.49 Oct 14
8 Oct 12—Oct 16 Random Variables and Their Probability Distributions. 4.1 4.1: 4.1, 4.7, 4.8, 4.9, 4.12 Oct 21
9 Oct 19 Review for Midterm 2.
9 Oct 21 Midterm 2.
9 Oct 23 Random Variables and Their Probability Distributions. The Bernoulli Distribution. The Binomial Distribution. 4.1, 4.2, 4.3 4.2: 4.19, 4.23, 4.41
R (Posted):  R4 		Oct 28
10 Oct 26—Oct 30 Independence of Random Variables. Distribution of a sum of independent random variables. Convolution of probability functions. Expected Value of Discrete Random Variables. Variance. 4.4, 4.5, 4.6 4.4: 4.43, 4.49, 4.51, 4.61, 4.63, 4.6: 4.67, 4.72, 4.73, 4.78, 4.79 Nov 4
11 Nov 2—Nov 6 Tchebysheff's Inequality. The Geometric Distribution. The Negative Binomial Distribution. The Poisson Distribution. The Hypergeometric Distribution. 4.7, 4.8, 4.9, 4.10 4.7: 4.89, 4.101, 4.8: 4.109, 4.110, 4.9: 4.125, 4.126, 4.127, 4.128, 4.132, 4.135, 4.10: 4.139, 4.143
R (Due):  R4 		Nov 11
12 Nov 9—Nov 13 The Moment-Generating Function. The Probabilty-Generating Function.
12 Nov 11 Veteran's Day - no class.
12   The Moment-Generating Function. The Probabilty-Generating Function. 4.11, 4.12
13 Nov 23—Nov 27 Continuous random Variables and Their Probability Distributions. 5.1, 5.2
14 Nov 30 Review for Midterm 3. Expected Values of Continuous Random Variables. The Uniform Distribution. The Exponential Distribution. 5.3, 5.4
14 Dec 2 Midterm 3.
14 Dec 4 The Gamma Distribution. The Normal Distribution. 5.5, 5.6 5.4: 5.41, 5.42, 5.43, 5.5: 5.65, 5.67, 5.6: 5.83, 5.85
R (Due):  R5 		Dec 9
15 Dec 7—Dec 9 Expectation of Discontinuous functions and Mixed Probability Distributions. Review before the Final Exam.
Finals Week Dec 15 (Tuesday) Final Exam, 10:30 am - 12:30 pm (regular room).