STATS/MATH 425 SECTIONS 007 & 008

Introduction to Probability

Fall 2013

Class Information

Days & Time:

Section 007: Tue, Thu 10:00 am -- 11:30 am
Section 008: Tue, Thu 2:30 pm -- 4:00 pm

Location:

Section 007: 513 Dennison
Section 008: 296 Dennison

Prerequisites: MATH 215 is a formal prerequisite. You should know Calculus (differentiation, integration, change of variables) well.
Description: You will learn basic concepts of probability and become aware of its diverse applications in various scientific and engineering disciplines. The emphasis is on concepts and problem-solving. Topics include axioms of probability, conditional probability, independence, random variables (both discrete and continuous), joint distributions, expectation, variance, covariance.
Textbook: A First Course in Probability (8th edition) by Sheldon Ross.
Ctools: You should access the Ctools class page for this course frequently. It will contain important announcements, posted homework assignments, discussion forum, and chat room.

Instructor Information

Name: Ambuj Tewari

Office: 454 West Hall

Office Hours: Tuesdays, 11:30 am - 1:00 pm and Thursdays, 12:30 pm - 2:00 pm

Email: tewaria@umich.edu

GSI information

Section 7	Section 8
Name: Jesus Arroyo	Name: Mikhail Yurochkin
Office Hours & Location: Mondays, 10-11:30am in the Science Learning Center, 1720 Chemistry Building and Wednesdays, 10-11:30am in 470 West Hall	Office Hours & Location: Fridays, 2-5pm in the Science Learning Center, 1720 Chemistry Building
Email: jarroyor@umich.edu	Email: moonfolk@umich.edu

Grading

The final grade in the course will be determined by your scores in homeworks, one midterm exam, and one final exam using the weights given below.

Homeworks (30%): There will be 11 homework assignments in all. I will drop your lowest score and use the remaining 10 assignments to calculate the grade. Late homework submissions will not be accepted unless you present a well-documented case of a medical or family emergency. You are encouraged to discuss problems with your classmates but you should always write up your own solutions. Copying solutions (from anywhere including classmates, internet, previous years’ solutions) is never permitted and any instances of academic dishonesty will be reported to the Dean’s office. Please show all steps in your calculations.
Midterm Exam (30%): This will be a closed-book exam (no notes, no calculator) held in class on Thu, October 17.
Final Exam (40%): This will be a closed-book exam (no notes, no calculator) held in our regular classroom (513 Dennison for Sec 7, and 296 Dennison for Sec 8) on the times given below. These times cannot be changed and are determined by the Office of the Registrar. The final exam will cover material from the entire course.

Section 007: Wed, December 18, 10:30 am -- 12:30 pm
Section 008: Fri, December 20, 1:30 -- 3:30

Accommodations for Students with Disabilities

If you think you need an accommodation for a disability, please let me know at your earliest convenience. Some aspects of this course, the assignments, the in-class activities, and the way the course is usually taught may be modified to facilitate your participation and progress. As soon as you make me aware of your needs, we can work with the Office of Services for Students with Disabilities (SSD) to help us determine appropriate academic accommodations. SSD (734-763-3000; http://www.umich.edu/sswd) typically recommends accommodations through a Verified Individualized Services and Accommodations (VISA) form. Any information you provide is private and confidential and will be treated as such.

Academic Integrity

Please familiarize yourself with the LSA Community Standards of Academic Integrity. The College of LSA expects all of its members to uphold these Standards.

Schedule

The tentative schedule for the semester is given below. It will most likely change as we move along. References of the form (x.y) refer to sections in the textbook.

Day	Plan
Sep 3	Basic principle of counting (1.2) Examples 2a, 2c, 2e Permutations (1.3) Example 3b Self-test 1 begin
Sep 5	Permutations (1.3) continued Self-test 1 continued Combinations (1.4) Basic formula Identity (4.1) Combinatorial proof of Binomial theorem
Sep 10	Combinations (1.4) continued Examples 4b, 4e Multinomial Coefficients (1.5) Examples 5a, 5b HW 1 out
Sep 12	Sample space and events (2.2) Examples of experiments and their sample spaces Operations (unions, intersections, complements) on events de Morgan’s laws Axioms of probability (2.3)
Sep 17	Axioms of probability (2.3) continued Examples 3a, 3b Proposition 4.1, 4.2 and 4.3 Example 4a HW 1 due
Sep 19	Inclusion-Exclusion principle (2.4) Sample spaces having equally likely outcomes (2.5) Examples 5a, 5b, 5c, 5d HW 2 out
Sep 24	Conditional Probabilities (3.2) Definition (Eq. (2.1)) Multiplication rule Examples 2b, 2d
Sep 26	Conditional Probabilities (3.2) continued Example 2h Bayes’ Formula (3.3) Examples 3a (both parts) HW 2 due HW 3 out
Oct 1	Bayes’ Formula (3.3) continued Examples 3c, 3k Independent Events (3.4) Example 4b
Oct 3	Independent Events (3.4) continued Example 4e Independence of multiple events Examples 4g, 4h HW 3 due HW 4 out
Oct 8	Random variables (4.1) Examples 1a, 1c Discrete random variables (4.2) probability mass function
Oct 10	Discrete random variables (4.2) continued Example 2a Cumulative Distribution Function Expected value (4.3) Examples 3a HW 4 due HW 5 out
Oct 15	NO CLASS (Fall Study Break)
Oct 17	MIDTERM EXAM Section 007: 10-11:30 in 513 Dennison Section 008: 2:30-4:00 in 296 Dennison
Oct 22	Expected value (4.3) continued Examples 3d Expected value of a function of a random variable (4.4) Example 4a, Proposition 4.1, Corollary 4.1 Definition of moments Variance (4.5) Definition, alternative formula Example 5a Standard deviation
Oct 24	Bernoulli random variables (4.6) Eq. (6.1) Expectation and variance of Bernoulli random variables Binomial random variables (4.6) Eq. (6.2) Example 6b Expectation and variance (4.6.1) Poisson random variable (4.7) Eq. (7.1) HW 5 due HW 6 out
Oct 29	Poisson random variable (4.7) continued Poisson as an approximation to Binomial when n is large, p small Example 7b MID-SEMESTER FEEDBACK
Oct 31	Expected value of sums (4.9) Example 9b Proposition 9.1, Corollary 9.2 Example 9d HW 6 due HW 7 out
Nov 5	Introduction to continuous random variables (5.1) Expectation and variance (5.2) Proposition 2.1 Corollary 2.1 The uniform random variable (5.3) Example 3a
Nov 7	Relationship between pdf and cdf The two equations right after Example 1c on page 189 Normal random variables (5.4) “an important fact” near the middle of page 199 Example 4a cdf of a standard normal HW 7 due HW 8 out
Nov 12	Normal random variables (5.4) continued Examples 4b Normal approximation to the Binomial (5.4.1) Example 4f
Nov 14	Exponential random variables (5.5) Examples 5a Memoryless property HW 8 due HW 9 out
Nov 19	Joint distribution functions (6.1) joint cdf joint pmf (for jointly discrete random variables) joint pdf (for jointly continuous random variables)
Nov 21	Joint distribution functions (6.1) continued Examples 1a, 1c, 1e HW 9 due HW 10 out
Nov 26	Independent random variables (6.2) Example 2c Proposition 2.1 Example 2f
Nov 28	NO CLASS (Thanksgiving break)
Dec 3	Conditional distributions: Discrete case (6.4) Examples 4a, 4b Conditional distributions: Continuous case (6.5) Examples 5a, 5b HW 10 due HW 11 out
Dec 5	Expectation of sums (7.2) Proposition 2.1, Equation (2.2) Examples 2a, 2c Covariance, variance of sums, correlations (7.4) Proposition 4.1 Definition of Covariance
Dec 10	Covariance, variance of sums, correlations (7.4) continued Proposition 4.2 Equation (4.1) Example 4b HW 11 due
Dec 18	SEC 007 FINAL EXAM (10:30-12:30 in 513 Dennison)
Dec 20	SEC 008 FINAL EXAM (1:30-3:30 in 296 Dennison)