Department of Mathematics

Pomona College

 

Math 151.  Probability           Fall 2013

 

Course Outline

 

Time and Place:         MWF  11:00 am – 11:50 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   8:05 am-8:55 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.   Readings and problem sets will be assigned at every lecture and collected on al alternate 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:   Thursday, December 19, 2013        9:00 am.

Place:   Seaver North Auditorium

Math 151.  Probability                                                                                  Fall 2013

 

Tentative Schedule of Lectures and Examinations

 

Date                            Topic

 

W        Sep.   4            Introduction:  A problem from statistical inference

F          Sep.   6            Sample Spaces

 

M         Sep.   9            σ-fields

W        Sep. 11            Probability function

F          Sep. 13            Probability function (continued)

 

M         Sep. 16            Independent events

W        Sep. 18            Conditional probability

F          Sep. 20            Continuous and discrete random variables

 

M         Sep. 23            Cumulative distribution function (cdf)

W        Sep. 25            Probability density function (pdf)

F          Sep. 27            Probability mass function (pmf)

 

M         Sep. 30            Review

W        Oct.   2            Review

F          Oct.   4            Exam 1

 

M         Oct.   7            Continuous random variable and probability density function (pdf)

W        Oct.   9            Expectation of a random variable

F          Oct.  11           Expectation of a function of a random variable

 

M         Oct.  14           Expectation of a function of a random variable (continued)

W        Oct.  16           Examples of random variables

F          Oct.  18           Moments, variance and moment generation function

 

M         Oct.   21          Fall Recess (No Class)

W        Oct.  23           Joint distribution functions

F          Oct.  25           Joint distribution functions (continued)

 

M         Oct.  28           Marginal distributions

W        Oct.  30           Marginal distributions (continued)

F          Nov.   1           Problems

 

M         Nov.   4           Review

W        Nov.   6           Exam 2

F          Nov.   8           Independent random variables

 

 

Date                            Topic

 

M         Nov. 11           mgf convergence theorem

W        Nov. 13           The Central Limit Theorem

F          Nov. 15           Simple random samples

 

M         Nov. 18           Mean and variance of random samples

W        Nov. 20           Sampling distribution 

F          Nov. 22           Conditional distribution

 

M         Nov. 25           Conditional expectation

W        Nov. 27           Problems

F          Nov. 29           Thanksgiving Recess

 

M         Dec.   2            Covariance and correlation

W        Dec.   4            Review

F          Dec.   6            Exam 3          

 

M         Dec.   9            Review

W        Dec. 11            Review

 

 

Th        Dec  19            Final Examination