STA 4321 – Mathematical Statistics I



STA 4321 – Introduction to Probability

STA 5325 – Fundamentals of Probability

Spring 2007

Instructor: Dr. Larry Winner

e-mail: winner@stat.ufl.edu

Office: 228 Griffin/Floyd

Office Hours: M 2:00-3:30, W 9:50-11:20

TA: Alex Savenkov: Office Hours: M3, W7, F4 @ 218 Griffin/Floyd

Textbook: Introduction to Probability and Its Applications, 2nd Ed, (1995). Richard L. Scheaffer, Duxbury.

Prerequisites: MAC 2311-2313 (or equivalent) and one introductory statistics course.

Course Description: This course is a calculus based introduction to probability theory.

General topics include:

Basic Probability (Chapter 2)

• Randomness (2.1)

• Set Notation (2.2)

• Probability (2.3)

• Counting Rules (2.4)

• Conditional Probability/Independence (2.5)

• Probability Rules (2.6)

• Odds, Odds Ratios/Relative Risk (2.7)

• Introduction to Simulation (2.8)

Discrete Probability Distributions (Chapter 3)

• Discrete Random Variables/Probability Distributions (3.1)

• Expected Values (3.2)

• Families of Discrete Distributions

• Bernoulli (3.3)

• Binomial (3.4)

• Geometric (3.5)

• Negative Binomial (3.6)

• Poisson (3.7)

• Hypergeometric (3.8)

• Moment-Generating Function (3.9)

• Probability-Generating Function (3.10)

• Simulation (3.12)

Continuous Probability Distributions (Chapter 4)

• Continuous RVs/Probability Distributions (4.1)

• Expected Values (4.2)

• Families of Continuous Distributions

• Uniform (4.3)

• Exponential (4.4)

• Gamma (4.5)

• Normal (4.6)

• Beta (4.7)

• Moment-Generating Functions (4.10)

• Simulation (4.12)

Multivariate Probability Distributions (Chapter 5)

• Bivariate & Marginal Distributions (5.1)

• Conditional Distributions (5.2)

• Independent Random Variables (5.3)

• Expected Values of Functions of RVs (5.4)

• Multinomial Distribution (5.5)

• Moment-Generating Functions (5.6)

• Conditional Expectations (5.7)

• Compounding (5.8)

Functions of Random Variables (Chapter 6)

• Method of Distribution Functions (6.2)

• Method of Transformations (6.3)

• Method of Conditioning (6.4)

• Method of Moment-Generating Functions (6.5)

• Order Statistics (6.6)

• Limit Theorems (Chapter 7)

• Convergence in Probability (7.2)

• Weak Law of Large Numbers (7.2)

• Convergence in Distribution (7.3)

• The Central Limit Theorem (7.4)

Grading: 5 In-Class Midterm exams, Project and Cumulative Final

▪ Exam 1: Friday, January 26

▪ Exam 2: Friday, February 16

▪ Exam 3: Wednesday, March 7

▪ Exam 4: Monday, April 9

▪ Exam 5: Wednesday, April 25

▪ Final Exam (30%)

MWF 5: Thursday, May 3 @ 12:30-2:30PM

MWF 6: Wednesday, May 2 @ 7:30-9:30AM

Course Policies (Read Carefully):

➢ All exams are closed book/closed notes. You will need a calculator.

➢ Your top 4 midterm exams will each count 15%, of grade, the cumulative final exam will count 30%, and project will count 10%.

➢ Problems will be assigned from each section as well as from chapter supplementary exercises. These will be representative of exam problems and will help you prepare for exams.

➢ Examples covered in class are also likely to appear on exams. It is your responsibility to keep up with all material, or you will find exams very difficult.

➢ The university scheduled the final exam time. Do not plan on leaving Gainesville prior to your final exam time.

➢ This course makes use of all Pre- and co-requisites, be prepared to use calculus (especially Chapters 4-6)

➢ No Make-up exams will be given with the exception of documented medical emergencies.

➢ Lectures are the time to ask questions. No questions regarding content will be answered during exams.

Practice Problems:

Section: Problems

Chapter 2

2.2: 1,2,3,4

2.3: 5,6,7,9

2.4: 11,13,14,15,17,18,19,20,21,23,25

2.6: 27,28,29,32,33,34,35,36,37,38,39,40,41,42,43,44,46

2.7: 48

2.9: 51,52,53,54,55,57,59,60,61,62,64,65,66,69,70,71,72,73,74,76,78,79

Chapter 3

3.1: 1,2,3,4,6,8,10

3.2: 11,12,15,17,19,20,21,22

3.4: 23,24,25,26,27,30,32,33,34,35,36,37,38,39

3.6: 40,41,42,43,45,46,47,49,52

3.7: 54,55,59,60,61,62,63,64,65,67,68

3.8: 70,71,75,76

3.10: 84,85,86,87,88,89

3.13: 95,97,98,102,103,106,109,112,113,116,117,119,120,122,124

Chapter 4

4.1: 1,2,3,5,6,7,8

4.2: 9,10,11,13,14

4.3: 15,16,18,24,25,26,27,28

4.4: 30,31,32,33,35,37,39,40,44

4.5: 45,47,49,51,53

4.6: 55,56,57,58,61,64,66,67,68,69

4.7: 73,74,75,76,79,80

4.10: 95,96,97,98

4.13: 102,103,105,106,107,110,111,114,115,116,119,120,122,123,124,125,127

Chapter 5

5.3: 1,2,3,4,5,6,7,8,11,13,14,15,16

5.4: 17,18,19,21,22,23,24,25

5.5: 26,27,28,29,31,33,34

5.6: 36,37,38,40

5.7: 41,42,43

5.9: 44,45,46,47,48,49,51,54,57,60,61,62,63,67,69,70,75,76

Chapter 6

6.2: 1,2,3,4,5,6,8

6.4: 9,10,11,12,13

6.5: 14,15,16,17,18,19

6.6: 21,22,24,25

6.8: 30,31,33,35,36,38,40,41

Chapter 7

7.3: 1,2,3,4,5

7.4: 7,8,11,17,18

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