Department of Mathematics

Pomona College

 

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.   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:    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