Stat/Math 414
Introduction to Probability Theory
MWF, 8:00–8:50am, 203 Willard
Prof. Ben Shaby
bshaby@psu.edu
313 Thomas
Office Hours: Tuesday 10:00–11:30am, Wednesday 2:00-3:00pm
Course Description: Probability spaces, discrete and continuous random variables, transformations, expectations, generating functions, conditional distributions, law of large numbers, central
limit theorems.
TA: Yifan Zhang (yxz192@psu.edu), office hours: Thursday 2:30–3:30pm in 301 Thomas
Text: Probability, 9th Edition
Author: Sheldon Ross; ISBN-13: 978-0-321-79477-2
Prerequisites: Fluency with elementary calculus (derivatives, integrals, etc).
Course Objectives:
• Be able to manipulate probability expressions involving independence, conditioning, etc.
• Become familiar with basic probability distributions and know in what context each is useful.
• Understand properties of expectations and conditional expectations.
• Develop reasoning skills and intuition about fundamental limit theorems.
Grade Distribution:
Weekly Assignments
Midterm 1
Midterm 2
Final Exam
20%
20%
20%
40%
Letter Grade Distribution: Students always ask if the class is graded on a curve. I am a
statistician—everything in life is on a curve.
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Course Policies:
• General
– Quizzes and exams are closed book, closed notes. Where appropriate, I will provide
formula sheets and tables.
– If you bomb an exam, no makeup exams will be given.
• Grades
– Grades in the C range represent performance that meets expectations; Grades in the
B range represent performance that is substantially better than the expectations;
Grades in the A range represent work that is excellent.
• Homework Assignments
– There will be weekly homework assignments, due in class on Fridays.
– No late homework will be accepted for any reason.
– I will not accept papers held together using some combination of folding and tearing the
corner. Use staples!
– The grader will carefully grade a subset of the assigned problems and scan the remainder
to ensure that they are finished. The graded problems will be worth a total of 10 points,
and completion of the un-graded problems will earn a total of 10 points. This makes
each assignment worth 20 points all together.
– No late assignments will be accepted under any circumstances.
– Assignments and solutions 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.
• Exams
– There will be two midtem exams, each worth 20% of the final grade. There will be no
homework assigned during the weeks the midterms occur.
– The final exam is comprehensive and represents 40% of the final grade.
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 particluar, 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 will 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-and-cooperation/Code-of-Mutual-Respect%20final.
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pdf) 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.
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Tentative Course Outline: (This could change, depending on the progress of the class.)
Week
Content
Week 1
• Basic combinatorics
• Reading assignment: 1.1–1.5
Week 2
• Axioms of probability, sample spaces
• Reading assignment: 2.1–2.5
Week 3
• Conditional probability, Bayes’s theorem
• Reading assignment: 3.1–3.3
Week 4
• Independent events, more on conditional probability
• Reading assignment: 3.3–3.5
Week 5
• Random variables, discrete r.v.s, expectations
• Reading assignment: 4.1–4.3
Week 6
• Expectations, variance, Bernoulli and Binomials r.v.s, moment generating
functions
• Reading assignment: 4.4–4.6, 7.7
• Midterm exam: Ross 1.1–1.5, 2.1–2.5, 3.1–3.5, 4.1–4.5.
Week 7
• Poisson, Geometric, Negative Binomial, Hypergeometric, others; expected values of sums
• Reading assignment: 4.7–4.9
Week 8
• Continuous r.v.s, Uniform, Normal distributions
• 5.1–5.4
Week 9
• Exponential, other continous (e.g. Gamma, Weibull etc.); transformations
• Reading assignment: 5.4–5.7
Week 10
• Joint distributions; independence, sums of independent r.v.s; conditional pmfs
• Reading assignment: 6.1–6.4
Week 11
• conditional pdfs, pmfs; order statistics; multivariate transformations
• Reading assignment: 6.4–6.7
• Midterm exam: Ross 4.6–4.9, 5.1–5.7, 6.1 (only for discrete r.v.s: joint pmfs,
marginal pmfs)
Week 12
• Expectations of sums; covariances
• Reading assignment: 7.1–7.4
Week 13
• Conditional expectations, law of iterated expectations
• Reading assignment: 7.5
Week 14
• Limit theorems, Chebyshev’s inequality, Weak Law of Large Numbers, Central
Limit Theorem
• Reading assignment: 8.1–8.3
Week 15
• Strong Law of Large Numbers, Inequalities
• Reading assignment: 8.4–8.5
Week 15
• Final exam
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