Department of Mathematics

Pomona College

 

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 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:    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