General Course Information  Course Content  Required Background  Software 
Textbooks  Required Work  Grading  Detailed Course Schedule 
Kevin Deng 
Justin Kim 
dengke@bc.edu 
kimavz@bc.edu 
OH: Thursday, 5PM7PM 
OH: Friday, 1PM3PM 
My colleague Bob Muller calls this policy the
'laptopfree classroom'. (For 'laptop', read 'laptop and
smartphone'.)
A successful class requires your attention,
engagement, and participation. You need to be prepared
to ask and answer questions during the lectures, and to
attend to the questions and answers of your fellow students
and of the instructor. That screen open to your email
or Facebook page distracts not only you, but the students
sitting behind you. For this reason, open laptops are
not permitted in the classroom, unless they are part
of some planned activity for which your computer is
required.
You say you're taking notes on that
laptop instead of shopping on Amazon? You should be aware
that (a) it is very difficult to take notes for this class
on a computer, given the large number of mathematical
symbols, formulas and diagrams that we use; and (b) taking
notes by hand is better for you. It is
acceptable to take notes on a tablet computer with a stylus.
Exceptions to this rule will be made for the
rare instances of inclass activities that require students
to use their computers. There will be one such activity on
the first day of class.
Date 
Topic 
Handouts and Lecture Notes 
Assignments

Week 1 January 1517 
A cointossing
experiment. Simulations in Python and matplotlib. 
Monkey
Tacos Installing and using the software NumPy reference matplotlib plotting reference Cointossing experiments (heavily commented Python code to demonstrate the plotting and numerical tools) How to prepare the homework (a mockup homework assignment). Nonrequired readingMore than you ever wanted to know about
flipping coins:
Is there such a thing as an unfair coin?
No, say these statistics professors. 
Assignment
1, due January 23 text file with PT's coin tosses (one of the homework problems) LaTeX source for assignment The class data from the cointossing experiment (Excel spreadsheet with macros, showing length of longest run and number of runs). The class data from the experiment last year. 
Week 2 January 2224 
Discrete probability
spaces, Independent events (2.1,2.2) 
Lecture
1Probability spaces Lecture 2Some worked examples; sampling with and without replacement; independent events. Simulation of two dice Simulation of drawing cards from a deck, pulling beans from a jar. 
Assignment 2, due January
30 LaTeX source for assignment 
Week 3 January 2931 
Counting (2.3) 
Lecture
3: Basic counting principles; birthdays Plot of birthday probabilities Lecture 4: Binomial coefficients 
Assignment 3, due February 8 LaTeX source for assignment .csv file containing the real birthday data Code for reading the .csv file 
Week 4 February 5February 7 
Discrete random variables. (3.13.4 and 3.6.1 on Expected value)  Lecture
5: Discrete random variables Simulating the roll of two dice using the CDF iPython notebook of this simulation (this is just an html view of the class demo, both inputs and outputs, not an active notebook that you can modify) 
Assignment 4, due February 20 LaTeX source for assignment 
Week 5 February 12February 14 
More discrete random
variables. Geometric distribution. Poisson distribution. Expected value. 
Lecture
6: Important discrete random variables Lecture 7: Expected value of a discrete random variable Lecture 8: Some worked examplesnumbers racket, coupon collector's problem, averagecase running time of quicksort. 

Week 6 February 19February 21 
More on expected value 

Week 7 February 2628 
First test Conditional Probability and Bayes's theorem (Chapter 6, but note that the textbook does conditional probability after continuous probability spaces, so the material here about continuous conditional probability can be skipped for now.) 
Last year's midterm Last year's midterm with solutions. (Advice: Don't look at this until you've tried to work the problems.) This year's midterm with solutions. Lecture 9: Conditional probability and Bayes's Theorem 
Assignment 5, part 1, due Friday, March 15 LaTeX source for assignment Assignment 5, part 2, due Monday, April 1 The data sets for Part 2 Support code for Part 2 
Spring break 

Week 8 March 1214 
Continuous sample spaces
and continuous random variables. 
Lecture
10: Continuous Probability Spaces Simulation of Buffon needle problem 
Assignment 6, due March 27 LaTeX source for assignment 
Week 9 March 1921 
Continuous sample spaces
and continuous random variables. 
Lecture
11: Continuous Random Variables Simulation of dartboard example (iPython notebook). Lecture 12: More on the exponential distribution 

Week 10 March 2628 
Variance, Markov's and Chebyshev's inequalities. Law of Large numbers 
Lecture
13: Variance, Markov's and Chebyshev's inequalities,
Law of Large Numbers 

Week 11 April 24 
Normal distribution and
Central Limit Theorem Second Test 
The second test from last
year The second test from last year, with solutions The test with solutions 
Assignment 7, due April 12 The 911 call dataset (CSV file) Code for reading the elapsed times from the data file. 
Week 12 April 911 
More on Central Limit
Theorem (Chapter 5) 
Normal distribution demo
(iPython notebook) Lecture 14: Normal distribution Part 1(approximation to binomial distribution) Lecture 15: Normal distribution Part 2 (Central Limit Theorem) Probability plots and normal distributions in natural data (iPython notebook) 
Assignment 8, due April 26 
Week 13 April 16 (just one class) 
Markov Chains (Chapter 9) 
Lecture 16: Markov Chains Part 1 (basics and analysis of absorbing chains) 
Assignment 9,
due May 2 
Week 14 April 2325 
Markov Chains 
Lecture 17:
Markov Chains Part 2 (analysis of regular Markov
chains) 

Week 15 April 30May 2 
Review 
The final exam
from 2018 Solutions to the 2018 final The final exam from 2014 (Note: Take the last question, which is about Markov chains, with a grain of salt! Parts (a) and (b) refer to some linear algebra that we did not study in detail this year. Part (d) can be solved without worrying about things like eigenvalues, just by solving a simple linear system.) Review problems from several years ago (ignore the next to last question about eigenvalues and principal components) Review problems with solutions 