Instructor: Eric Slud, Statistics program, Math. Dept.
Office: MTH 2314, x5-5469, email email@example.com,
Please fill out the on-line Evaluation form on this Course and instructor, by Tuesday Dec. 10, at http://CourseEvalUM.umd.edu. Thank you.
Also please note that I am scheduling a review session for the Final Exam, for anyone who wants it, on the afternoon of Wednesday December 11 4:30-6pm, as an extended office hour in my office at MTH 2314.
Course Text: Sheldon Ross,
A First Course in Probability, 10th ed., Pearson.
We will cover Chapters 1-8, and some of Chapter 10 on Simulation as time permits.
Syllabus: This semester's syllabus, based on the Ross 10th edition.
Overview: This course is a solid introduction to the formulation and manipulation of probability models, leading up to proofs of limit theorems: the law of large numbers and the central limit theorem. It is a gateway course to serious study of mathematical statistics and graduate-level applied statistics. Key topics characterizing this course as opposed to more elementary introductions to Probability include joint distributions and change-of-variable formulas for them; conditional expectation and its applications; and the formal proofs of limit theorems.
Prerequisite: Math 240-241 or Math 340-341.
Course requirements and Grading: there will be graded homework sets (one every 2 weeks, 5 altogether) which together will count 20% of the course grade; (two or three) 15-minute quizzes in-class that will together count 10%; 2 tests that will count 20% each; and a final exam that will count 30%.
Notes and Guidelines. (a) Homeworks should be handed in as hard-copy in-class, except for
possible occasional due-dates on Fridays when you may submit them electronically, via email,
in pdf format. A percentage deduction (at least 15%) of the overall HW score will generally be made for late papers.
Homework 1 (due Friday 9/6, 5pm): Reading is all of Chapter 1 of 10th edition.
Homework 2 (due Wednesday 9/25, 5pm; 11 problems in all): Reading consists of Chapters 2, 3
and 4 through 4.8.3.
Homework 3 (due Wednesday 10/23, 5pm; 13 problems in all): Reading: Chapter 4 Sections 4.9, 4.10,
all of Chapter 5, and Chapter 10 through 10.2.1.
Homework 4 (due Monday 11/18, 5pm; 12 problems in all): Reading: Chapter 6, omitting Sections 6.6 and 6.8, and Chapter 7 through Section 7.5.
Homework 5 (12 problems in all) will be due Monday, December 9, 5pm in class: Reading:
Chapter 7, Section 7.3 and 7.5 through end, Chapter 8, and Simulation Handout which is the same as the second Handout pdf under handouts (3) below.
(1.) Practice (i.e., sample) problems for Test 1 on Wednesday, October 9, are posted here. Tests in this course are closed-book, so you should practice and commit to memory all formulas (or derivations) that you think you will need.
(2.) Practice (i.e., sample) problems for Test 2 on Wednesday, November 20, are posted here. Tests in this course are closed-book, so you should practice and commit to memory all formulas (or derivations) that you think you will need. There is also a linked summary of topics for Test 2.
(3.) Here are two handouts here, respectively on Transformation of Random Variables and on Random Number Generation and Simulation. These topics are very important for concrete illustration of the course material, as they allow us to generate and interpret `artificial data' to illustrate the meaning of our Probability Limit Theorems (Law of Large Numbers, Central Limit Theorem). In addition, Simulation gives us an `experimental' avenue to calculate via artificial data probabilities which may be too difficult to figure analytically.
(4.) Here is a handout on Normal
Approximation to Binomial Distribution containing a word-problem worked example, as well as some numerical
examples of the quality of the normal approximation to the Binomial. A graph comparing the distribution function
values of Binom(100,.3) with its approximating normal distribution N(30,21) can be found here.
(5.) Here is another handout, on Binomial approximation
to Hypergeometric random variables, and the Poisson approximation to the Binomial. In addition, some simulated-data results are given to show that the expectations and probability mass functions behave as they should according to the relative-frequency interpretation of probabilities.