STA 4321/5325 – Introduction to Probability

Section 5516 (4321)

MWF Period 4, FLO 100

Fall 2015

# Instructor: Dr. Larry Winner

e-mail:  winner@stat.ufl.edu

## Office Hours: (See Class Website for Update)

##### TA: (See Class Website for Update)

Textbook: Mathematical Statistics With Applications, 7th Ed, (2008). Wackerly, Mendenhall, and. Scheaffer, Brooks/Cole.

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

·         Basic Probability (Chapter 2)

·         Introduction (2.1)

·         Probability and Inference (2.2)

·         Set Notation (2.3)

·         Probability: Discrete Case (2.4)

·         Probability: Sample-Point Method (2.5)

·         Counting Rules (2.6)

·         Conditional Probability/Independence (2.7)

·         Probability Rules (2.8)

·         Probability: Event-Composition Method (2.9)

·         Law of total Probability and Bayes’ Rule (2.10)

·         Numerical Events and random Variables (2.11)

·         Random Sampling (2.12)

·         Discrete Probability Distributions (Chapter 3)

·         Discrete Random Variables/Probability Distributions (3.1-3.2)

·         Expected Values (3.3)

·         Families of Discrete Distributions

·         Bernoulli and Binomial (3.4)

·         Geometric (3.5)

·         Negative Binomial (3.6)

·         Hypergeometric (3.7)

·         Poisson (3.8)

·         Moment-Generating Function (3.9)

·         Probability-Generating Function (3.10)

·         Tchebysheff’s Theorem (3.11)

·         Simulation

·         Continuous Probability Distributions (Chapter 4)

·         Continuous RVs/Probability Distributions (4.1-4.2)

·         Expected Values (4.3)

·         Families of Continuous Distributions

·         Uniform (4.4)

·         Normal (4.5)

·         Gamma (4.6)

·         Beta (4.7)

·         Moment-Generating Functions (4.9)

·         Tchebysheff’s Theorem (4.10)

·         Mixed Probability Distributions (4.12)

·         Simulation

·         Multivariate Probability Distributions (Chapter 5)

·         Bivariate & Marginal Distributions (5.1-5.2)

·         Marginal and Conditional Distributions (5.3)

·         Independent Random Variables (5.4)

·         Expected Values of Functions of RVs (5.5)

·         Special Theorems (5.6)

·         Covariance (5.7)

·         Expected Value and Variance of Linear Functions of RVs (5.8)

·         Multinomial Distribution (5.9)

·         Bivariate Normal Distribution (5.10)

·         Conditional Expectations (5.11)

·         Functions of Random Variables (Chapter 6)

·         Probability Distribution of Functions of RVs (6.1-6.2)

·         Method of Distribution Functions (6.3)

·         Method of Transformations (6.4)

·         Method of Moment-Generating Functions (6.5)

·         Multivariable Transformations Using Jacobians (6.6)

·         Order Statistics (6.7)

·         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: 4 In-Class Midterm exams and 2 Projects (5% Each)

§  Exam 1: Friday, September 18 (22.25%)

§  Exam 2: Friday, October 9     (22.25%)

§  Exam 3: Wednesday, November 4          (22.25%)

§  Exam 4: Monday, December 7    (22.25%)

Course Policies (Read Carefully):

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

Ø  Problems will be assigned from each. These will be representative of exam problems and will help you prepare for exams.

Ø  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.

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

Ø  No Make-up exams will be given with the exception of medical emergencies or academic reasons.

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

Practice Problems:

Section: Problems

Chapter1

1.2: 3,5,7

1.3: 9,11,12,19,21

Supplementary Exercises: 22,23,24,27,29,31,33,36

Chapter 2

2.3: 1,2,3,4,5,6,7,8

2.4: 9,10,11,13,14,15,17,19,21,22,23,24

2.5: 26,28,29,30,31,33

2.6: 35,36,37,38,39,40,41,43,45,46,50,53,55,57,61,68,69*

2.7: 71,72,73,75,77,79,81,82,83

2.8: 85,86,89,90,92,95,97,98,104,105

2.9: 111,112,113,115,117,120,121

2.10: 125,129,133,135

2.11: 139,140,141

Supplementary Exercises: Read as many as possible, and confirm you know how to set the problem up.

Chapter 3

3.2: 1,3,4,5,9,10,11

3.3: 12,14,15,16,19,20,21,23,24,27,30,31,33,34

3.4: 35,37,38,39,41,43,44,45,48,51,53,55,56,57,59,62

3.5: 67,68,70,71,73,74,83,84

3.7: 103,104,105,106,109,113,114

3.8: 121,122,123,125,126,127,131,134,137,138,139,142,143,144

3.9: 145-155,158,159,161

3.11: 167,168,169ab,177

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

Supplementary Exercises: Read as many as possible, and confirm you know how to set the problem up.

Chapter 4

4.2: 1,3,5,6,8,9,11-17,19

4.3: 20-31,33

4.4: 38-44,49,51,52,57

4.5: 58a-e,59,60,60,61,62,66a,67,68a,69,70,73,75,77,80

4.6: 81,82,88-92,103,104,105a,106a,107a,109-112

4.7: 123a,124a,125-130,133a-c

4.9: 136-140,143,144

4.10: 146-152

Supplementary Exercises: Read as many as possible, and confirm you know how to set the problem up.

Chapter 5

5.2: 1,2,4,5,6-10,12-15,17,18

5.3: 19,20,22,23,24,25,27,28,30,31,32,33,34,35,37,39*,42*,

5.4: 43,45,46,48,49,50,51,53,56,57,59,61,63,65*,68,69,71

5.6: 72,74,75,76,77,78,81,83,85**,87    **e makes use of next section

5.7: 89,91,92,94,95,96,97,99,100,101*

5.8: 102,103,105-108,110-114,116,118

5.9: 119,120,122-125

5.11: 133,134,136,138,139,140,142

Supplementary Exercises: Read as many as possible, and confirm you know how to set the problem up.

Chapter 6

6.3: 1-8,10,11,12,15,17

6.4: 23-28,31-35

6.5: 37-43,46,47,49-52,53,55,57,59

6.6: 63,64

6.7: 72-75,80-83,87,88

Supplementary Exercises: Read as many as possible, and confirm you know how to set the problem up.