Department of Mathematics
Math 151. Probability Fall 2014
Course Outline
Time and Place: MWF 9:00 am – 9:50 am
Seaver Commons 102
Instructor: Dr.
Adolfo J. Rumbos
Office:
Mudd Science Library 106
Phone/e-mail: ext. 18713 / arumbos@pomona.edu
Office Hours: MWF 10:05 am-10:55 am, TR 10:30 am – 11:30am,
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.
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: Thursday, December 18,
2014 9:00 am – 11:00 am.
Place: Seaver Commons 102
Math 151. Probability Fall 2014
Tentative Schedule of Lectures and
Examinations
Date Topic
W Sep. 3 Introduction: A problem from statistical inference
F Sep. 5 Sample
Spaces
M Sep. 8 σ-fields
W Sep.
10 Probability function
F Sep.
12 Probability function (continued)
M Sep. 15 Independent events
W Sep.
17 Conditional probability
F Sep.
19 Continuous and discrete random
variables
M Sep. 22 Cumulative
distribution function (cdf)
W Sep.
24 Probability density function (pdf)
F Sep.
26 Probability mass function (pmf)
M Sep. 29 Continuous
random variable and probability density function (pdf)
W Oct. 1 Review
F Oct. 3 Exam 1
M Oct. 6 Expectation
of a random variable
W Oct. 8 Expectation of a
function of a random variable
F Oct.
10 Expectation of a function of a random
variable (continued)
M Oct. 13 Moments,
variance and moment generation function
W Oct.
15 Joint
distribution functions
F Oct.
17 Joint
distribution functions (continued)
M Oct. 20 Fall Recess
W Oct.
22 Marginal
distributions
F Oct.
24 Independent
random variables
M Oct. 27 Independent random variables
(continued)
W Oct.
29 The Poisson Distribution
F Oct.
31 Limiting
distributions
M Nov. 3 Limiting
distributions (continued)
W Nov. 5 Review
F Nov. 7 Exam
2
Date Topic
M Nov. 10 mgf convergence theorem
W Nov.
12 Convergence in distribution
F Nov.
14 Convergence in Probability
M Nov. 17 The Central Limit Theorem
W Nov.
19 Applications of the Central Limit
Theorem
F Nov.
21 Applications of the Central Limit
Theorem (continued)
M Nov. 24 Random
samples
W Nov.
26 Sampling distributions
F Nov.
28 Estimation
M Dec. 1 Estimation
(continued)
W Dec. 3 Review
F Dec. 5 Exam 3
M Dec. 8 Review
W Dec.
10 Review
Th Dec. 18 Final Examination