Important external links
Class 1: January 17th
Orientation.
First-Day Handout: Unique 53850 (1pm)
First-Day Handout: Unique 53855 (2pm)
Class 2: January 19th
Equally likely outcomes
(Section
1.1).
Homework #1 – due on Friday, January 26th
Class 3: January 22nd
Distributions (Section 1.3).
Wikipedia: Set notation
The R-script from class: Long-term proportions
Class 4: January 24th
Definition of
probability (Section
1.3).
Class 5: January 26th
More on probability.
Binomial coefficients.
Wikipedia: Standard \(52-\) card deck
Class 6: January 29th
De Méré’s paradox. Even
more on probability.
Wikipedia: De Méré’s paradox.
The R-script from class: A loaded tetrahedron with histograms and bar plots
Class 7: January 31st
Even even more on
probability.
(Enrichment material) MCMC Revolution by legendary Persi Diaconis
Class 8: February 2nd
Conditional probability
and the multiplication formula (Section 1.4).
Wikipedia: Groundhog day
Problem Set #1: Problems
Wikipedia: The Monty Hall problem
Homework #2 – due on Friday, February 9th
Class 9: February 5th
Independence and
probability trees (Section
1.4).
Problem Set #1: Solutions
Bayes’ rule (Section
1.5).
Class 10: February 7th
More on the Bayes rule
(Section
1.5).
In-Term One: Topics
Practice for In-Term One – problems
Practice for In-Term One – solutions
Class 11: February 9th
Bayes’ rule
practice.
Class 12: February 12th
Sequences of events
(Section
1.6).
Class 13: February 14th
In-Term One
In-Term One – solutions
Class 14: February 16th
Geometric distribution
[cont’d].
Mathematica demonstration: The geometric distribution
Problem Set #2: Problems
Problem Set #2: Solutions
The binomial distribution (Section 2.1).
Homework #3 – due on Friday, February 23rd
Class 15: February 19th
More on the binomial
distribution (Section
2.1).
Wikipedia: The binomial theorem
Wikipedia: Pascal’s triangle
Mathematica demonstration: The binomial distribution
Homework #4 – due on Friday, March 1st
Class 16: February 21st
Even more on the
binomial distribution (Section
2.1).
The normal distribution (Section
2.2).
Standard Normal Distribution Areas from the Wolfram Demonstrations Project by Ian McLeod
Class 17: February 23rd
More on the normal
distribution (Section
2.1).
Class 18: February 26th
More on the normal
distribution (Section
2.1).
The Normal Distribution from the Wolfram Demonstrations Project by Ian McLeod
Area of a Normal Distribution from the Wolfram Demonstrations Project by Eric Schulz
The normal approximation to the binomial distribution (Section 2.2).
Class 19: February 28th
More on the normal
approximation to the binomial distribution (Section 2.2).
Mathematica demonstration: The Normal Approximation to the Binomial Distribution
Homework #5 – due on Friday, March 8th
In-Term Two: Topics
Practice for In-Term Two: Problems
Practice for In-Term Two: Solutions
Class 20: March 1st
The Poisson approximation
(Section
2.4).
Wikipedia: The Poisson distribution
Mathematica demonstration: The Poisson Distribution
Mathematica demonstration: The Poisson Approximation to the Binomial Distribution
Class 21: March 4th
Introduction to random
variables (Section
3.1).
Homework #6 – due on Friday, March 22nd
Class 22: March 6th
In-Term Two
In-Term Two – solutions
Class 23: March 8th
Functions of random
variables (Section
3.1).
The cumulative distribution function (cdf) (Section 4.5).
Class 24: March 18th
More on random variables
(Section
3.1).
Homework #7 – due on Friday, March 29th
Class 25: March 20th
Functions of pairs of
random variables (Section
3.1).
Class 26: March 22nd
Independent pairs (Section 3.1).
Class 27: March 25th
Expectation (Section 3.2).
Homework #8 – due on Friday, April 5th
Class 28: March 27th
Markov’s and Chebishev’s
inequalities (Section
3.2).
Class 29: March 29th
Standard deviation and the
normal approximation (Section
3.3).
Homework #9 – due on Friday, April 12th
Extra credit #1 – due on Friday, April 26th and worth an extra 3 points on your final score in the course
Class 30: April 1st
The covariance formula (Section 3.3).
Class 31: April 3rd
The Central Limit Theorem
(Section
3.3).
Class 32: April 5th
Discrete distributions (Section 3.4).
Homework #10 – due on Friday, April 19th
Class 33: April 8th
Solar Eclipse
Class 34: April 10th
More on discrete
distributions (Section
3.4).
Homework #11 – due on Friday, April 26th
Class 35: April 12th
The Poisson distribution
(Section
3.5).
Suggested textbook problem: 3.5.3.
Class 36: April 15th
Continuous distributions
(Section
4.1).
Class 37: April 17th
Expectations of continuous
random variables.(Section
4.1).
Suggested textbook problems: 4.1.4, 4.1.6, 4.5.4, 4.5.5, 4.5.6 a,b,c
The normal distribution [revisited] (Section 4.1).
In-Term Three: Topics
Practice for In-Term Three: Problems
Practice for In-Term Three: Solutions
Class 38: April 19
More on the central limit
theorem.(Section
4.1).
The exponential distribution (Section 4.2).
Class 39: April 22nd
More on the exponential
distribution (Section
4.2).
Suggested textbook problem: 4.2.1
Class 40: April 24th
In-Term Three
In-Term Three – solutions
Class 41: April 26th
Change of variable (Section 4.4).
Suggested textbook problems: 4.4.3, 4.4.6
Class 42: April 29th
Jointly uniform random
variables and joint densities (Section 5.1 and
5.2).
Suggested textbook problems: 5.1.3, 5.1.4
Independent normal random variables (Section 5.1 and
5.2).
The Final Exam: Topics
Practice for the Final Exam – problems
Practice for the Final Exam – solutions
