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.