Department of Mathematics
Math 151.
Probability Fall 2016
Course Outline
Time and Place: TR 8:10 am – 9:25 am Millikan 1021
Instructor: Dr.
Adolfo J. Rumbos
Office:
Andrew 2287
Phone/e-mail: ext. 18713 / arumbos@pomona.edu
Office Hours: MWF 10:05 am-10:50 am, TR 10:00 am – 11:00am,
or
by appointment
Text: Probability and Statistics,
by Morris H. DeGroot and Mark J. Schervish, Adison Wesley
Course Website: http://pages.pomona.edu/~ajr04747/
Prerequisites: Multivariable
Calculus or Vector Calculus, and Linear Algebra.
Course
Description. This course is an introduction to the
theory and applications of Probability; special attention will be given to
applications relevant to statistical inference.
A solid knowledge of multivariable calculus and linear algebra will be assumed. The course topics are listed in the attached
tentative schedule of lectures and examinations.
Assigned Readings and Problems. Readings and problem sets will be assigned and
collected on weekly basis. Students are
strongly encouraged to work on every assigned problem. Late homework assignments will not be graded.
Grading
Policy. Grades will be based on the homework, three
50-minute examinations, plus a comprehensive final examination. The overall score will be computed as
follows:
homework 20%
three 50-minute exams 50%
final examination 30%
Final
Examination.
Time: Monday, December 12,
2016 7:00 pm – 9:00 pm.
Place: Millikan 1021
Math
151. Probability Fall
2016
Tentative Schedule of Lectures and
Examinations
Date Topic
T Aug. 30 Introduction: A problem from statistical inference
R Sep. 1 Sample
Spaces and σ-fields
T Sep.
6 Probability function
R Sep.
8 Independent
events
T Sep. 13 Conditional probability
R Sep.
15 Continuous and discrete random
variables
T Sep. 20 Cumulative
distribution function (cdf)
R Sep.
22 Probability mass function (pmf) and
probability density function (pdf)
T Sep. 27 Review
R Sep.
29 Exam 1
T Oct.
4 Expectation
of a random variable
R Oct. 6 Expectation
of a function of a random variable
T Oct. 11 Moments,
variance and moment generation function
R Oct.
13 Joint
distribution functions
T Oct. 18 Fall Recess
R Oct.
20 Marginal
distributions and independent random variables
T Oct. 25 Independent random variables
(continued)
R Oct.
27 The
Poisson Distribution
T Nov.
1 Review
R Nov. 3 Exam 2
T Nov.
8 Limiting distributions and the mgf convergence theorem
R Nov.
10 Convergence in distribution and
convergence in Probability
T Nov. 15 The
Central Limit Theorem
R Nov.
17 Applications of the Central Limit
Theorem
T Nov. 22 Random
samples and Sampling distributions
R Nov.
24 Thanksgiving
Recess
T Nov. 29 Review
R Dec. 1 Exam
3
T Dec. 6 Review