Mathematics 464

Theory of Probability

Fall 2009

Course Syllabus

 

 

 

 

Week

 

 

Dates

 

 

Topic

 

 

Pages

 

 

 

  

 

 

1

 

 

25 Aug – 27 Aug

 

 

Experiments with Chance

Sample Space

Events

Probabilities

Probability Spaces

Conditional Probability

 

4-9

 

 

       HW#1

 

       HW#1-Solns

  

 

 

2

 

 

      1 Sept – 3 Sept

 

Independence

Partition Theorem

Continuity of the Probability Measure

Counting

 

             9-16

 

 

  Notes on Counting

 

 

 

 

 

 

       3

 

 

       8 Sept – 10 Sept

 

Probability Mass Functions

Discrete RV Catalog

            

             22-28

 

Quiz 1: 8 Sept

  

         HW#2

         HW#2-Solns

 

 

4

 

 

     15 Sept – 17 Sept

Discrete RV Catalog (cont’d)

 

            

              24-28

Notes on Negative Binomial Distribution

 

 Quiz 2:  17 Sept

 

 

5

 

 

      22 Sept – 24 Sept

Functions of Discrete RVs

Expected Value

Cond. Expectation and the

Partition Function

 

            28 - 34

          HW#3

          HW#3-Solns

  

 

 

6

 

 

      28 Sept – 1 Oct

 

 Multivariate Discrete Distributions

 

 

             36 - 38

 Quiz 3: 1 Oct

 

  

 

 

7

 

 

       6 Oct – 8 Oct

 Review for Midterm

 

 

 

 

Midterm 1: 8 Oct

Midterm1-solns

 

 

8

 

 

     13 Oct – 15 Oct

 Independence of Discrete RVs

 Sums of Random Variables

 Generating Functions

 

 

 

             38 - 46

 

 

 

 

 

  

 

 

9

 

 

     20 Oct – 22 Oct

 Generating Functions

 Moments

 Sums of Independent RVs

 

 

 

              46 - 53

         HW#4

         HW#4-Solns

 

 

10

 

 

     27 Oct – 29 Oct

 Distribution Functions,

 Density Functions,  

 Continuous RVs

 

 

 

56 - 65

 

 

    Quiz 4: 29 Oct

 

 

 

11

 

 

      3 Nov – 5 Nov

 

  Continuous RVs, Expectations, Variance

  Order Statistics

             65-70

    HW#5

    HW#5-Solns

 

 

12

 

 

     10 Nov – 12 Nov

 

  Waiting Times, Joint Distributions and  

  Densities for Continuous RVs, 

  Marginal Density Functions, Sums of

  Continuous RVs, Changes of Variables, 

  Conditional Density Functions, 

  Expectations

              75-92

 

    Quiz 5:  10 Nov

 

     HW#6

     HW#6-Solns

 

 

13

 

 

     17 Nov – 19 Nov

  Conditional Expectation and the

  Bivariate normal distribution

 

  Review for Midterm 2

 

               92-96

 

 

 

   Quiz 6:  17 Nov

 

 

14

 

 

      24 Nov

 

 

 

 

 

 

 

 Midterm 2: 24 Nov

 Midterm2-solns

 

 

15

 

 

       1 Dec – 3 Dec

 

   Moments, Variance & Covariance, 

   Moment Generating Functions, Weak

  

            

              104-115

  Notes on Moment Generating Functions

 

      HW#7

      HW#7-Solns

 

 

16

 

 

       8 Dec

 

   Law of Large Numbers

   Central Limit Theorem

    

              124-132

  Quiz 7:  8 Dec

 

 

17

 

 

 

    14 Dec -17 Dec

 

 

   

 

 

 

 Review Session: 14 Dec

 4 pm Math East 246

 

 Final Exam: 17 Dec

  2 – 4 PM,  PAS 224