Department of Mathematics
Math 151. Probability Spring 2014
Course Outline
Time and Place: MWF 9:00 am – 9:50 am
Seaver North Auditorium
Instructor: Dr.
Adolfo J. Rumbos
Office:
Mudd Science Library 106
Phone/e-mail: ext. 18713 / arumbos@pomona.edu
Office Hours: MWF 11:05 am-11:55 am, TR 9:00 am – 10:00am,
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 presupposed.
The course topics are listed in the attached tentative schedule of
lectures and examinations.
Assigned Readings and Problems.
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: Wednesday, May 14,
2014 9:00 am.
Place: Seaver North
Auditorium
Math 151. Probability Spring 2014
Tentative Schedule of Lectures and
Examinations
Date Topic
W Jan
22 Introduction: A problem from statistical inference
F Jan
24 Sample Spaces
M Jan 27 σ-fields
W Jan 29 Probability
function
F Jan 31 Probability
function (continued)
M Feb 3 Independent
events
W Feb 5 Conditional probability
F Feb
7 Continuous and
discrete random variables
M Feb 10 Cumulative
distribution function (cdf)
W Feb
12 Probability density
function (pdf)
F Feb
14 Probability mass
function (pmf)
M Feb 17 Continuous random variable and
probability density function (pdf)
W Feb 19 Review
F Feb 21 Exam
1
M Feb 24 Expectation of a random variable
W Feb 26 Expectation
of a function of a random variable
F Feb 28
Expectation of a function
of a random variable (continued)
M Mar 3 Moments,
variance and moment generation function
W Mar
5 Joint distribution
functions
F Mar
7 Joint distribution
functions (continued)
M Mar 10 Marginal distributions
W Mar 12 Independent
random variables
F Mar 14 Independent
random variables (continued)
M Mar 17 Spring
Recess
W Mar 19 Spring Recess
F Mar 21 Spring Recess
M Mar 24 Review
W Mar 26 Exam
2
F Mar 28 César Chávez Day
Date Topic
M Mar 31 The Poisson Distribution
W Apr
2 Limiting distributions
F Apr
4 mgf
convergence theorem
M Apr 7 Convergence
in distribution
W Apr
9 Convergence in
Probability
F Apr
11 The
Central Limit Theorem
M Apr 14 Applications
of the Central Limit Theorem
W Apr
16 Applications of the
Central Limit Theorem (continued)
F Apr
18 Random samples
M Apr 21 Sampling
distributions
W Apr
23 Estimation
F Apr
25 Estimation (continued)
M Apr 28 Review
W Apr
30 Review
F May
2 Exam
3
M May 5 Review
W May
7 Review
W May 14 Final
Examination