Math 477 - Mathematical Theory of Probability - Summer 2014

Instructor: Christopher Sadowski

Email: sadowski at math dot rutgers dot edu

Office: Hill Center 620

Office Hours: Monday 3-5pm or by appointment

Text: A First Course in Probability, Ninth Edition, by Sheldon Ross

Location: Tillet 251, Livingston Campus

Meeting times: Monday, Wednesday, and Thursday 6:00-7:55 p.m.

Grading:

All students enrolled in Rutgers courses are expected to be familiar with and abide by the academic integrity policy (http://academicintegrity.rutgers.edu/policy-on-academic-integrity).

Violations of this policy are taken very seriously.

-20% Homework

-20% Midterm 1 (July 9, 2014) Solutions

-20% Midterm 2 (July 30, 2014) Solutions

-40% Final Exam (August 13, 2014)

Homework: There will be weekly homework assigned, listed here. All homework assigned and due on the day of a midterm will be on material relevant to that midterm.

Please show all work and explain all reasoning behind your solution. Writing down an answer without an explanation will result in no credit for the problem!

Homework 1, due 7/2/2014:

Chapter 1: 7,8,13, 28, 31

Chapter 2: 3, 6, 8, 10, 13

Homework 2, due 7/9/2014:

Chapter 2: 18, 23, 41, 43, 47

Chapter 3: 4, 5, 16, 37, 43, 56

Homework 3, due 7/16/2014:

Chapter 4: 7, 14, 17, 18, 19, 21, 25, 30

Homework 4, due 7/23/2014:

Chapter 4: 35, 38, 48, 74, 75, 78

Chapter 5: 3, 6, 13

Homework 5, due 7/30/2014:

Chapter 5: 15, 16, 18, 28, 35

Chapter 6: 9, 13, 23, 26, 31

Homework 6, due 8/6/2014:

Chapter 6: 39, 40, 41, 42

Chapter 7: 5, 6, 11, 13

Homework 7, no due date. We will review these on 8/11/2014. This is practice for the final:

Chapter 7: 37, 38, 53, 75, 76

Chapter 8: 1, 2, 4, 13, 15

Syllabus (subject to change as the course progresses):

Week 1:

June 23, 2014

1.2: The Basic Principle of Counting

1.3: Permutations

1.4: Combinations

1.5: Multinomial Coefficients

June 25, 2014

1.6: The Number of Integer Solutions of Equations

2.2: Sample Spaces and Events

June 26, 2014

The Inclusion-Exclusion Principle for enumerating sets

2.3: Axioms of Probability

2.4: Some Simple Propositions

For fun: BBC article about the birthday problem and the World Cup

Week 2:

June 30, 2014

2.5: Sample spaces having equally likely outcomes

2.6: Probability as a continuous set function

July 2, 2014

3.2 Conditional Probability

3.3: Bayes's Formula

July 3, 2014

3.4: Independent Events

3.5: P( . | F) is a Probability

Week 3:

July 7, 2014

4.1: Random Variables

4.2: Discrete Random Variables

For fun: The probability of rolling sums on 3+ dice.

July 9, 2014

EXAM 1: Will cover all material up to and including July 3, 2014.

July 10, 2014

4.3: Expected Value

4.4: Expectation of a Function of a Random Variable

Week 4:

July 14, 2014

4.5: Variance

4.6: The Bernoulli and Binomial Random Variables

July 16, 2014

4.7: The Poisson Random Variable

4.8: Other Discrete Probability Distributions

July 17, 2014

5.1: Introduction

5.2: Expectation and Variance of Continuous Random Variables

5.3: The Uniform Random Variable

Week 5:

July 21, 2014

5.4: Normal Random Variables

5.5: Exponential Random Variables

July 23, 2014

5.7: The Distribution of a Function of a Random Variable

6.1: Joint Distribution Functions

July 24, 2014

6.2: Independent Random Variables

6.3: Sums of Independent Random Variables - Only normal random variables

Week 6:

July 28, 2014

6.3: Sums of Independent Random Variables - continued

6.4: Conditional Distributions: Discrete Case

6.5: Conditional Distributions: Continuous Case

July 30, 2014

EXAM 2: Will cover all material from July 7 up to and including July 24, 2014.

July 31, 2014

7.2: Expectation of Sums of Random Variables

7.3: Moments of the Number of Events that Occur

Week 7:

August 4, 2014

7.4: Covariance, Variance of Sums, and Correlations

7.5: Conditional Expectation

August 6, 2014

7.7: Moment Generating Functions

8.2: Chebyshev's Inequality and the Weak Law of Large Numbers

August 7, 2014

8.3: The Central Limit Theorem

8.4: The Strong Law of Large Numbers

Week 8:

August 11, 2014

Review

August 13, 2014

FINAL EXAM: The exam is 3 hours long and will cover all material from the course.