STAT 416 Fall 09: Probability

Course Description:

This introductory course will cover the basics of probability theory targeted for undergraduate students in statistics, mathematics, and actuarial sciences.  Among the topics covered will be
For students interested in taking actuarial exams, the course will cover topics appearing on Exam 1/P.

General Information:

Course Number: 29227 STAT 41600 - 002
Also cross-listed as MATH 41600 - 002 (CRN: 23364)

Lectures: Monday, Wednesday, and Friday, 9:30-10:20am, 119 University Hall

Instructor: Professor Sergey Kirshner
Office Hours: Monday 1:30-2:30pm, Thursday 3:00-4:00pm in HAAS 118 (or by appointment)

Textbook: Introduction to Probability by George Roussas, Academic Press, 2007 (Required) (errata)

The course will cover Chapters 1-4, 5, 6-8, 10.1-10.2, 11.1-11.3, 12.

Additional Resources:

Textbooks:
Introduction to Probability by Charles M. Grinstead and L. Laurie Snell, American Mathematical Society, 1997 (suggested as an additional reference, available for free download from the website)

A First Course in Probability by Sheldon Ross, Prentice Hall, 7th edition, 2006 (suggested as an additional reference, especially for students preparing for actuarial exams; editions different from suggested are as good; offers a great number of examples of varying difficulty)

Announcements:

8/21: Homework 1 is posted, due on Monday, August 31.
8/26: Fixed a typo in problem 2.12 of homework 1.
8/28: Since we did not cover Section 2.4 yet, problems 2.4.1, 2.4.3, 2.4.5, and 2.4.7 are transferred to homework 2.
8/30: Homework 2 is posted, due on Friday, September 11.
8/31: Solutions for homework 1 are posted on Blackboard Vista.  If you find any mistakes or typos, please let me know.
9/9: Since we did not finish Section 3.3 (specifically, probability density functions) yet, some of the problems from homework 2 (3.3.3, 3.3.5, 3.3.11, 3.3.13, 3.3.17) were transferred to homework 3.
9/9: Practice quiz 1 with a solution is posted.
9/10: Homework 3 is posted, due on Friday, September 18.  Grades for homework 1 are posted on Blackboard Vista.
9/12: Quiz 1 graded.  Scores and solutions are posted on Balckboard Vista.  Solution for homework 2 is also posted.
9/16: Problems 4.2.1, 4.2.5, and 4.2.9 are moved from homework 3 to homework 4.
9/17: Homework 4 is posted, due on Friday, September 25.
9/21: Homework 2 grades are posted on Blackboard Vista.  Problem 5.1.5 is transferred from homework 4 to homework 5.
9/22: Grades for homework 3 are posted on Blackboard Vista.
9/24: Homework 5 is posted, due on Friday, October 2.  Per request of several students, I included several even-numbered exercises; the solutions for these exercises are available at the end of the textbook.
9/28: Practice Midterm 1 is posted.  Solutions posted as well.
10/6: Midterm 1 graded, scores and solutions posted on Blackboard Vista
10/6: Homework 6 is posted, due on Friday, October 16.
10/8: As was stated in the email sent out to the course mailing list, the score for midterm 1 will be weighed with a factor 1.2 when the final grade is calculated.
10/8: Problem 6.1.30 (homework 6) contains a typo, please reload the homework set for a correction.
10/8: Practice quiz 2 has been posted together with a solution.  Quiz is designed for 20 minutes.
10/15: Quiz 2 will cover the material from the last quiz up to (and including) Friday, Oct. 9 lecture.
10/15: Scores for homeworks 1-5 are posted on Blackboard Vista.  Please let the instructor know if any of your scores are missing or are entered incorrectly.
10/15: Important: Midterm 2 has been rescheduled (see schedule).  Please let the instructor know as soon as possible if the new midterm time introduces a conflict.
10/15: Errata for the textbook has been posted.  Some of the answers in the book are not accurate.
10/16: Quiz 2 graded.  Scores (Quiz 2 and extra 2 separately) and solutions are posted on Blackboard Vista.
10/16: Homework 7 is posted, due on Friday, October 23.  Solutions for homework 6 are posted on Blackboard Vista.
10/16: Important: As was announced in lecture, it is possible to earn extra 20 points for the course by making a 10 minute in-class presentation illustrating or explaining one of the concepts related to topics in the course.  Due to time limitation, only one presentation is possible per lecture (and no more than one presentation per student), so slots and topics are limited.  Currently agreed on topics with corresponding dates are posted on the schedule.
10/19: Important: Final exam schedule has been posted.  It will take place on Friday, December 18, 3:30-5:20pm in BRWN 1154.
10/20: Homework 7 contained a typo in each of Ross 4.79 and 5.10 problems.  Please download the corrected version (as of 9:30am on 10/20).
10/21: Deadline for homework 7 is pushed back to Monday, October 26.  The rest of the homeworks will stay on the previous schedule.
10/22: Homework 8 is posted, due on Friday, October 30.
10/26: Solution for homework 7 is posted on Blackboard Vista.
10/29: Homework 9 is posted. It is due on November 9.
11/01: Practice quiz 3 has been posted together with a solution.  Quiz is designed for 20 minutes.  Please time yourself while solving it and provide me with feedback on how long it took you to solve it.
11/04: Homework 9 due date has been pushed back to Monday, November 9.
11/08: Quiz 3 has been graded.  Solutions and grades are posted on Blackboard Vista.
11/08: Practice Midterm 2 is posted together with solutions.
11/08: Homework 10 is due on Wednesday, November 18, 2009.
11/10: Problems 8.1.3 and Ross 7.75 have been dropped from homework 10.
11/16: Midterm 2 graded; solution and scores are posted on Blackboard Vista.
11/17: Solution for homework 10 is posted on Blackboard Vista.
11/17: Homework 11 is posted, due on Wednesday, December 2, 2009.


Grading:

The course will be evaluated on a point system.


 Number of assignments
 Points each
Total
Homeworks
 12 - 2 lowest scores = 10
 15
 150
Quizzes
 4 -1 lowest score = 3
 50
 150
Midterms
 2
 175
 350
Final
 1
 350
 350
Total

1000

Grading scheme and course policies are described in the course syllabus.

Practice Exams:

Practice quiz 1, solution
Practice midterm 1, solution
Practice quiz 2, solution
Practice quiz 3, solution
Practice midterm 2, solution

(Very) Tentative schedule:

Week
 Monday
 Wednesday
 Friday
1
 Aug 24: Course overview, motivation (Ch. 1)
 Aug 26: Sample spaces and events, sets, identities (Ch. 2.1, 2.2)
 Aug 28: Inclusion-exclusion principle (2.2), random variables (Ch 2.3)
2
 Aug 31: HW 1 due, combinatorics (Ch. 2.4)
 Sep 2: Combinatorics (2.4)
 Sep 4: Definition of probability (Ch 3.1), basic properties (3.2)
3
 Sep 7: Labor Day
 Sep 9: Distributions of random variables, probability mass functions (3.3) Sep 11: HW 2 due, Quiz 1, probability density functions (3.3)
4
 Sep 14: Conditional probability, chain rule for probabilities (4.1)total probability theorem, Bayes rule (4.1) Sep 16: Total probability theorem, Bayes rule (4.1) Sep 18: HW 3 due, Independence (4.2), conditional independence
5
 Sep 21: Independence (4.2), conditional independence Sep 23: Expected value of a r.v.(5.1), variance standard deviation of a r.v. (5.1)
 Sep 25: HW 4 due, expected value, moments, moment generating functions (5.1), Chebyshev's inequality (5.2)
6
 Sep 28: Moment generating functions (5.1), quantiles, median, mode (5.3)
 Sep 30: Bernoulli trials, binomial distribution (6.1.1) Oct 2: HW 5 due, binomial distribution (6.1.1), midterm information and brief review
7
 Oct 5: Midterm 1, Chapters 1-5, up to (including) Sep 28 lecture
 Oct 7: Midterm overview
 Oct 9: Geometric distribution (6.1.2), negative binomial distribution (handout)
8
 Oct 12: Fall Break
 Oct 14: Poisson distribution (6.1.3), hypergeometric dsitribution (6.1.4)
 Oct 16: HW 6 due, Quiz 2, Poisson distribution (6.1.3)
9
 Oct 19: Hypergeometric distribution (6.1.4), uniform distribution (6.2.5)
 Oct 21: Normal approximation to binomial distribution (handout),  Gaussian distribution (6.2.4) (presentation: Wyatt Clarke)
 Oct 23: Gaussian distribution (6.2.4)
10
 Oct 26: HW 7 due, exponential distribution (6.2.2) (presentation: Ure Ganbold)
 Oct 28: Gamma distribution (6.2.1) Transformation of a single random variable (11.1), log-normal distribution, Chi-square distribution (6.2.3) (presentation: Kicho Yu; topic: Carl Friedrich Gauss)
 Oct 30: HW 8 due, jointly distributed random variables (7.1)
11
 Nov 2: Marginal and conditional distributions and densities (7.2) Nov 4: Marginal and conditional distributions and densities (7.2), independent random variables (10.1) Nov 6: Quiz 3, independent random variables (10.1)
12
 Nov 9: HW 9 due, sums of independent random variables (10.2) Nov 11: Sums of independent random variables, convolution (10.2), joint moment generating functions (8.1) Nov 13: Transformation of several random variables (11.2-11.3), midterm information and brief review
13
 Nov 16: Midterm 2, 8:00-9:15pm, B155 Lawson Building (regular lecture is replaced by question/answer session)
 Nov 18: HW 10 due, midterm overview, expectation of a sum of random variables
 Nov 20: Expectation of a sum of random variables (presentation: Jiayin Wang)
14
 Nov 23: Variance of a sum of random variables, covariance (8.2) (presentation: Emily Raymond)
 Nov 25: Thanksgiving Break
 Nov 27: Thanksgiving Break
15
 Nov 30: Covariance, correlation (8.2), bivariate normal distribution (9.3) (presentation: Mike Hunter)
 Dec 2: HW 11 due, conditional expectation, conditional variance (7.2) (presentation: Ben Berning)
 Dec 4: Quiz 4
16
 Dec 7: Law of large numbers (12.1) (presentation: Jake Roth)
 Dec 9: Central limit theorem (CLT) (12.2) (presentation: Nik Datsenka)
 Dec 11: HW 12 due, review by Prof. Alice Vatamanelu (Sergey is away)
17

Final Exam (comprehensive) Friday, December 18, 3:20-5:20pm, BRWN 1154

Last modified: 19 Nov 2009