Download Introduction to Probability Theory - Penn State Department of Statistics

Stat/Math 414 Introduction to Probability Theory
Section 4 Fall Semester 2016
Lecture: MWF 9:05-9:55 a.m. in 260 Willard
Instructor: Professor Dennis Pearl
Office: 412 Thomas Bldg.
Office Hours: W 10:10 a.m.; Thursday 1:00 p.m. or by appointment
Email: [email protected]
TA: Vincent Pisztora
Office Hours: Monday 5-6 p.m.; Friday 11:30 a.m.-12:30 p.m.
Place: 320 Thomas Bldg.
Email: [email protected]
Course Description: Probability spaces, discrete and continuous random variables,
transformations, expectations, generating functions, conditional distributions, law of large
numbers, central limit theorems.
Learning Objective: To understand basic probability concepts and appreciate how they apply to
examining the uncertainties in real applications.
Text: A First Course in Probability (9th Edition) by Sheldon Ross
ISBN-13: 978-0-321-79477-2
Most of chapters 1 through 8 of the text will be covered.
Please do not buy earlier editions since the problems are different.
Prerequisites: Fluency with elementary calculus (derivatives, integrals, etc…)
Course Policies:


Grade Components:
Weekly Assignments
Online Quiz 1
Online Quiz 2
Midterm 1 (Sep. 30)
Midterm 2 (Nov. 4)
Final Exam
25% (250 points)
5% (50 points)
5% (50 points)
18% (180 points)
18% (180 points)
29% (290 points)
Course web page: You will find your grades, homework assignments, solutions, lecture
notes, announcements, a discussion board, and other course content on the ANGEL page.
Please check it on a regular basis.
• General
– Quizzes are open book. Midterm and Final Exams are closed book and closed notes.
However, I will provide formula sheet(s) and tables.
Grading Scale: The tentative final letter grading will follow the guidelines below
F
D
C
C+
B-
B
B+
A-
A
0%
50%
65%
73%
77%
80%
85%
88%
91%
It is possible that the grade distribution will be lowered slightly depending on the results of
the exams. All grades will be available in the ANGEL grade book.
• Homework Assignments
– There will be weekly homework assignments, due in class on Fridays.
– Assignments are not accepted late, without prior approval from the
instructor, except in cases of a documented emergency. Also, no assignment can be
accepted after solutions are posted. Thus, if a documented emergency creates a
situation where you cannot turn in your work before solutions are posted – that
assignments’ grade will be taken based on your percentage on the next exam.
– Be sure to write your name on each page of your assignments and to use staples
to hold them together.
– The grader will carefully grade a subset of three assigned problems and scan
the remainder to ensure that they are finished. The three graded problems will be worth a
total of 11 points (one at 5 pts and two at 3 points), and completion of the seven ungraded
problems will earn a total of 14 points (2 points each). This makes each assignment worth
25 points all together.
– The lowest grade of 11 assignments will be dropped.
– Assignments and solutions for all problems will be available on ANGEL.
– Start the assignments early, and go to office hours if you have trouble.
– You are allowed and even encouraged to work with other students in the class.
However, each student must turn in his/her own work, and in no case is it ever acceptable
to simply copy directly from another person’s work. Extra Credit Homework Assignments: You will have an opportunity to earn up to 5% (50
points) towards your overall course grade through extra credit assignments. The extra credit
assignments will provide a review of the more challenging course content leading into each exam
and will be due on September 28 (15 points worth before the first midterm); November 2 (15
points worth before the second midterm); and December 9 (20 points worth before the final
exam). The extra credit assignments will all be graded on correctness for all problems.
• Exams
– There will be two midterm exams, each worth 18% of the final grade. There will
be no homework assigned during the weeks the midterms occur as that is when the
extra credit is due. Midterms will be in lecture and we will have a review session in
the evening within a few days of each test. A formula sheet will be provided in
advance for each exam (midterms & final) and you may add your own annotations
to that.
– The first quiz will be between the two midterms and the second quiz will be between
the second midterm and the final. They will be online and multiple choice.
– The final exam is comprehensive and represents 29% of the final grade. Addressing Issues of Differing Abilities: Any student who feels they may need
an accommodation based on the impact of a disability should contact the instructor
privately to discuss your specific needs. Students with documented disabilities
must also contact the Office of Disability Services (ODS) in 116 Boucke Building
(phone: 863-1807) to coordinate reasonable accommodations for the course. For
further information regarding ODS, please visit the Office for Disability Services
Web site at http://equity.psu.edu/ods/.
In order to receive consideration for reasonable accommodations, you must
contact the disability services office, participate in an intake interview, and provide
documentation: (see the documentation guidelines at http://equity.psu.edu/studentdisability-resources/guidelines).
Academic Integrity: All Penn State and Eberly College of Science policies
regarding academic integrity apply to this course. See
http://www.science.psu.edu/academic/Integrity/Policy.html for details.
In particular, on exams,
each student must complete his/her own work without aiding or receiving aid from anyone else
in any way. Examples of infractions that result in disciplinary action are listed under ”Categories
of infractions” on the ECOS academic integrity page.
ECOS Code of Mutual Respect: The Eberly College of Science Code of Mutual
Respect and Cooperation (http://science.psu.edu/climate/code-of-mutual-respect-andcooperation) embodies the values that we hope our faculty, staff, and students possess and will
endorse to make the Eberly College of Science a place where every individual feels respected
and valued, as well as challenged and rewarded.
Feedback: I will ask for your feedback at regular intervals during the semester, but feel free to
give me your comments at any time. I want to continue to make Stat/Math 414 a better course
and will take your thoughtful criticism seriously.
Tentative Course Outline and Textbook Readings
(this could change depending on the progress of the course and your feedback)
Week
Topics (Textbook Readings)
Week 1 • Basic combinatorics, set operations, sample spaces
• Reading assignment: 1.1–1.5, 2.1–2.2
Week 2 • Axioms of probability, conditional probability, independent events
HW #1 • Reading assignment: 2.3–2.5, 3.1–3.2
Week 3 • Bayes’ theorem, more on conditional probability
HW #2 • Reading assignment: 3.3–3.5
• Labor Day holiday on Monday
Week 4 • Random variables, discrete random variables, expectations
HW #3 • Reading assignment: 4.1–4.3
Week 5 • More on expectations, variance, CDFs, discrete moment generating functions
HW #4 • Reading assignment: 4.4–4.6
Week 6 • Bernoulli and Binomials random variables
Extra
• Review for midterm
Credit • Midterm exam Friday September 30: Ross 1.1–1.5, 2.1–2.5, 3.1–3.5, 4.1–4.6.
Week 7 • Poisson, Geometric, Negative Binomial, Hypergeometric, others; expected values of
HW #5 sums
• Reading assignment: 4.7–4.9
Week 8 • Continuous random variables, Uniform, Normal distributions
HW #6 • Reading assignment: 5.1–5.4
Week 9 • Exponential, other continuous (e.g. Gamma, Weibull etc.); transformations
HW #7 • Reading assignment: 5.4–5.7
Week 10 • Joint distributions; independence, sums of independent r.v.s; conditional pmfs
HW #8 • Reading assignment: 6.1, 6.2, 6.4
Week 11 • Conditional pdfs, order statistics, multivariate transformations
Extra
• Reading assignment: 6.5–6.7
Credit • Midterm exam Friday November 4: Ross 4.6–4.9, 5.1–5.7, 6.1, 6.2, 6.4
Week 12 • Expectations of sums; covariances
HW #9 • Reading assignment: 7.1–7.4
Week 13 • Conditional expectations, law of iterated expectations
HW #10 • Reading assignment: 7.5
Have a great Thanksgiving break!
Week 14 • Limit theorems, Chebyshev’s inequality, Weak Law of Large Numbers, Central
HW #11 Limit Theorem
• Reading assignment: 8.1–8.3
Week 15 • Strong Law of Large Numbers, Inequalities
Extra
• Reading assignment: 8.4–8.5
Credit
Week 16 Final Exam (comprehensive)