Department of Mathematics
Math 151.
Probability Spring 2008
Course Outline
Time and
Place: MWF
10:00 am - 10:50 am
Millikan 207
Instructor:
Dr. Adolfo J. Rumbos
Office: Andrew 259
Phone/e-mail: ext. 18713 / arumbos@pomona.edu
Office
Hours: MWF 9:15 am – 9:50 am; Tu 9:15 am – 11:10 am;
or by appointment
Text: Probability and Statistical,
by Morris H. DeGroot and Mark J.
Schervish. Adison Wesley
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
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: Tuesday, May 13 8:00 am - 11:00 am.
Place: Millikan 207
Math 151. Probability Spring
2008
Tentative Schedule of Lectures and
Examinations
Date Topic
W Jan.
23 Introduction: A problem from statistical inference
F Jan.
25 Sample Spaces
M Jan. 28 σ-fields
W Jan.
30 Probability function
F Feb.
1 Probability
function (continued)
M Feb. 4 Independent events
W Feb.
6 Conditional
probability
F Feb.
8 Continuous
and discrete random variables
M Feb. 11 Cumulative
distribution function (cdf)
W Feb.
13 Probability density
function (pdf)
F Feb.
15 Probability mass
function (pmf)
M Feb. 18 Expectation
of a random variable
W Feb.
20 Review
F Feb.
22 Exam 1
M Feb. 25 Expectation
of a function of a random variable
W Feb.
27 Variance
F Feb.
29 Moments
M Mar. 3 Moment generating function (mgf)
W Mar.
5 Examples of random
variables
F Mar.
7 Examples of discrete
distributions
M Mar.
10 Examples of continuous
distributions
W Mar. 12 Joint
distribution functions
F Mar. 14 Joint distribution functions (continued)
M Mar.
17 Spring Recess
W Mar. 19 Spring
Recess
F Mar. 21 Spring Recess
M Mar.
24 Marginal distributions
W Mar. 26 Marginal
distributions (continued)
F Mar. 28 Cesar Chavez Day
(no class)
Date Topic
M Mar.
30 Review
W Apr.
2 Exam
2
F Apr.
4 Independent
random variables
M Apr. 7 mgf
convergence theorem
W Apr.
9 mgf convergence
theorem (continued)
F Apr.
11 The Central Limit
Theorem
M Apr. 14 Simple
random samples
W Apr.
16 Mean and variance of
random samples
F Apr.
18 Sampling distribution
M Apr. 21 Conditional
distribution
W Apr.
23 Conditional
expectation
F Apr.
25 Covariance and
correlation
M Apr. 28 Covariance
and correlation (continued)
W Apr.
30 Review
F May
2 Exam 3
M May
5 Review
W May
7 Review
Tu May
13 Final Examination