Announcements
 The final examination will be available on Friday, March 9 and due on Thursday, March 15 at Noon. There will be a review session on Saturday, March 10 in the Baxter Lecture Hall from 11:00 a.m. to 1:00 p.m., hosted by Jane Panagaden. Final review notes
 There is an auxiliary web page at www.hss.caltech.edu/~kcb/Courses/Ma3/ Right now it contains only notes on this site, but it may be better organized.
 The midterm examination will be available on Friday, February 2 and due on Tuesday, February 6 at 4:00 pm. There will be a review session on Saturday, February 3 at 1:00 in Baxter Lecture Hall. Midterm review notes
 There will be a Math 3 Ombuds meeting will be on Friday February 16 from 12 – 1. Let me know if you wish to volunteer.
Meeting Time and Location
Monday, Wednesday, and Friday
10:00  10:55 am
Baxter Lecture Hall
Instructor Contact Information and Office Hours
205 Baxter Hall
x4218
Office hours: 1:30–3:00, Fridays
TA Contact Information and Office Hours
TA 
Office 
Office Hours and Location 
Recitation Section Time and Location 
Hélène Rochais (Head TA) 
1K Math Building 
Friday 5:30  7:30 pm
B111 Downs 
Section 3  10 am B127 GCL
Section 9  9 am B127 GCL 
Tamir Hemo 
1D Math Building 
Friday 4:30  5:30 pm
B111 Downs 
Section 4  10 am 269 LAU 
Yuhui Jin 
1A Math Building 
Thursday 8  9 pm
B111 Downs 
Section 8  2 pm 142 KCK 
Jane Panagaden 
1H Math Building 
Monday 5  6 pm
B111 Downs 
Section 1  9 am 102 STL 
Sunghyuk Park 
1C Math Building 
Thursday 5  6 pm
B111 Downs 
Section 5  10 am 102 STL 
Nathaniel Sagman 
1B Math Building 
Monday 6  7 pm
B111 Downs 
Section 7  1 pm B122 GCL 
Forte Shinko 
1E Math Building 
Saturday 4  5 pm
B111 Downs 
Section 2  9 am 269 LAU 
Jim Tao 
2M Math Building 
Monday 10  11 pm
B111 Downs 
Section 6  1 pm 155 ARM 
Assignments
Date Posted 
Assignment 
Due Date 
Solutions 
Jan 3 
HW 0 
Jan 4, 8:00 pm 

Jan 8 
HW 1

Jan 16, 4:00 pm


Jan 16 
HW 2 
Jan 23, 4:00 pm 

Jan 14 
HW 3 
Jan 30, 4:00 pm 

Feb 7 
HW 4 
Feb 13, 4:00 pm


Feb 14  HW 5  Feb 20, 4:00 pm   Feb 21  HW 6  Feb 27, 4:00 pm   Feb 28  HW 7  Mar 6, 4:00 pm 

Exams
Course Description
Introduction to the fundamental ideas and techniques of probability theory and statistical
inference.
Probability will be covered in the first half of the term (using Pitman) and statistics (using Larsen
and Marx) in the second half (see below for information regarding textbooks). Main topics covered
are:
 Properties of probability
 Independence, conditional probability, Bayes' Law
 Random variables, distributions, densities, and expectation
 Joint distributions, marginals, covariance, correlation
 The Law of Large Numbers
 The Central Limit Theorem
 Order statisitics
 Important distributions
 Bernoulli, Binomial
 Uniform
 Normal (Gaussian)
 Exponential, Poisson
 Gamma, Beta, Chisquare
 Conjugate prior/posterior pairs
 Introduction to stochastic processes
 Random walk
 Markov chains
 Martingales
 Estimation of parameters
 Consistency, unbiasedness
 Maximum likelihood estimation
 Confidence intervals
 CramérRao lower bound
 Testing statistical hypotheses
 Significance tests
 Likelihood ratio tests
 Monotone Likelihood Ratio Property and the NeymanPerson Lemma
 Type I and Type II errors
 Power and assurance
 Critical values
 Specification tests
 KolmogorovSmirnov
 chisquare test, Fisher's exact test
 Linear regression analysis
 Gauss MarkovTheorem
 ANOVA
 Nonparametric tests
 Wilcoxon, MannWhitney, KruskalWallis
 Spearman rank correlation
Prerequisites
Ma 1abc. In addition, some familiarity with a scientific computing language or program (e.g.,
Mathematica, Matlab, NumPy, Octave, R) is assumed.
Textbooks
The required textbooks for the course are:
 Jim Pitman. 1993. Probability. Springer, New York, Berlin, and Heidelberg. ISBN: 0387979748.
 Richard J. Larsen and Morris L. Marx. 2012. An Introduction to Mathematical Statistics and Its Applications, fifth edition. Prentice Hall. ISBN: 0321693949.
There will be additional readings from time to time, either as handouts or articles available on line.
There are other books that you may find useful for this course or perhaps later in life. Here are, in no particular order, some of my recommendations.
 Robert V. Hogg, Elliot A. Tanis, and Dale Zimmerman. 2015. Probability and Statistical Inference. Pearson, Boston. ISBN: 9780321923271. This is a nicely written introduction that I am evaluating to see if it can replace the two books above.
 Alex Reinhart. 2015. Statistics Done Wrong: The Woefully Complete Guide. No Starch Press, San Francisco. ISBN: 9781593276201. This short (129 pages) book is written for scientists and covers many common misinterpretations of statistical methods and results in the analysis of scientific data.
 Calvin Dytham. 2011. Choosing and Using Statistics: A Biologist's Guide. WileyBlackwell. ISBN: 9781405198394. This is a
cookbook and reference geared toward biologists, but is a useful reference for almost everyone.
 David E. Matthews and Vernojn T. Farewell. 2015. Using and Understanding Medical Statistics. Karger, Basel. ISBN: 9783318054583.
 Robert B. Ash. 2008. Basic Probability Theory. Dover, Mineola, New York. Reprint of the 1970 edition published by John Wiley and Sons. ISBN: 0486466280. This book, being published by Dover, is very affordable. (I think it's still just under $20.) The first chapter, especially sections 1.4 through 1.7 are very good at explaining how to count for combinatorial problems.
 John B. Walsh. 2012. Knowing the Odds: An Introduction to Probability. American Mathematical Society, Providence, Rhode Island. ISBN: 9780821885321. I almost used this as the textbook for the course, but decided to stay with the status quo.
 Kai Lai Chung and Farid AitSahlia. 2003. Elementary Probability Theory with Stochastic Processes and an Introduction to Mathematical Finance.SpringerVerlag, New York, Heidelberg, and Berlin. ISBN: 9780387955780. This is a very wellwritten introduction to probability theory. Chapter 3 on counting is especially good.
 Richard Isaac. 1995. The Pleasures of Probability. SpringerVerlag, New York, Berlin, and Heidelberg. ISBN: 038794415X. Another good introduction to probability theory, but a bit too eccentric to use as the main text for this course.
Modern statistical practice is computationally intensive, but this course is not especially so. But you will have to use computers to do some of the assignments. Many of the people on campus that I have talked to recommend the statistical programming language R (the open source alternative to AT&T's S ). Mathematica 9 and later claims to be highly integrated with R , but I haven't tried it yet. Others I have talked to rave about NumPy , an extension of Python that provides much of the functionality of Matlab . Still others continue to use other packages because they have invested a lot of effort in learning to use them. (I myself use Mathematica because I started using it in 1992, so my recommendation of R falls into the category of "do as I say, not as I do.") My son recommends R and this video as an endorsement.
Here are a couple of highly recommended books on R that I mostly have not read. But I find the first two to be useful.
 Claus Thorn Ekstrom. 2011. R Primer. Chapman & Hall/CRC Press. Available for online reading from the Caltech Library.
 Paul Teetor. 2011. R Cookbook. O'Reilly Media. ISBN: 9780596809157.
 Joseph Adler. 2012. R in a Nutshell, 2nd edition. O'Reilly Media. ISBN: 9781449312084.
 Alain F. Zuur, Elena N. Ieno, and Erik H. W. G. Meesters. 2009. A Beginner's Guide to R. Springer Science+Business Media, New York. ISBN: 9780387938363.
 Peter Dalgaard. 2008. Introductory Statistics with R, second edition. Springer Science+Business Media, New York. ISBN: 9780387790534
Policies
 Late Work:

As a rule, late work is not accepted. This is to protect the TAs, who are talented hardworking
students, just as you are. At the discretion of the Head TA, late homework turned in the day it is
due, but after the 4:00 pm deadline will be accepted with a 25% penalty. If there are
extenuating circumstances, you must notify the Head TA by midnight the night before it is due and you
must get a note from the from the Dean supporting the extension.
 Grading:

Your course grade will be based on the weekly homework (40%), the midterm (25% or 35%), and the
final (35% or 25%). The weights on the final and midterm will put the greater weight on the better
exam.
This year I am continuing the following practice. Each assignment will contain zero or more
optional exercises. They are optional in the following sense: Grades will calculated without taking
the optional exercises into account, but the maximum grade will be an A. If you want an A+, you will
have to earn an A and also accumulate sufficiently many optional points. No collaboration is
allowed on optional exercises.
As this course may only be taken for a letter grade, no one will be excused from the final.
 Homework:

Homework will be typically be due at 4:00 pm on Tuesdays in the appropriate homework box outside
133 – 119 Downs. (Assignment 0 is a major exception.) Problems (and later solutions) will be posted on this course
webpage. You are encouraged to start the homework well in advance of the due date in order not to
risk missing the deadline. Homework is turned in to locked boxes, so it can safely be submitted as
soon as it is completed.
 Collaboration:

Collaboration is allowed on the homework, but your writeup must be in your own words and may not
be copied. The exception is that no collaboration is allowed on optional exercises. Collaboration is
not allowed on the exams. Please ask for clarification if anything is unclear.
*Information is subject to change*
Collaboration Policies

Homework 
Exams 
You may consult: 


Course textbook (including answers in the back) 
yes 
yes 
Other books 
yes 
NO 
Solution manuals 
NO 
NO 
Internet 
NO 
NO 
Your notes (taken in class) 
yes 
yes 
Class notes of others 
yes 
NO 
Your hand copies of class notes of others 
yes 
yes 
Photocopies of class notes of others 
yes 
NO 
Electronic copies of class notes of others 
yes 
NO 
Course handouts 
yes 
yes 
Your returned homework / exams 
yes 
yes 
Solutions to homework / exams (posted on webpage) 
yes 
yes 
Homework / exams of previous years 
NO 
NO 
Solutions to homework / exams of previous years 
NO 
NO 
Emails from TAs 
yes 
NO 
You may: 


Discuss problems with others 
yes 
NO 
Look at communal materials while writing up solutions 
yes 
NO 
Look at individual written work of others 
NO 
NO 
Post about problems online 
NO 
NO 
For computational aids, you may use: 


Calculators 
yes 
yes 
Computers 
yes 
yes 
* You may use a computer or calculator
as a tool, but you must justify and explain what you
asked the computer to do. Simply attaching your computer code and
output is not an acceptable justification or explanation. 
Updating...
Ċ Kim Border, Mar 9, 2018, 7:01 PM
Ċ Kim Border, Jan 2, 2018, 9:11 PM
Ċ Kim Border, Jan 8, 2018, 8:37 AM
Ċ Kim Border, Jan 16, 2018, 12:56 PM
Ċ Kim Border, Jan 24, 2018, 8:40 AM
Ċ Kim Border, Feb 7, 2018, 6:03 PM
Ċ Kim Border, Feb 15, 2018, 5:07 PM
Ċ Kim Border, Feb 21, 2018, 3:27 PM
Ċ Kim Border, Feb 28, 2018, 9:14 AM
Ċ Kim Border, Feb 2, 2018, 9:52 AM
Ċ Kim Border, Jan 17, 2018, 1:14 PM
Ċ Kim Border, Jan 17, 2018, 1:14 PM
Ċ Kim Border, Jan 31, 2018, 2:41 PM
Ċ Kim Border, Jan 22, 2018, 1:51 PM
Ċ Kim Border, Jan 17, 2018, 1:14 PM
Ċ Kim Border, Jan 19, 2018, 12:22 PM
Ċ Kim Border, Feb 11, 2018, 12:24 PM
Ċ Kim Border, Jan 24, 2018, 12:41 PM
Ċ Kim Border, Jan 24, 2018, 1:47 PM
Ċ Kim Border, Jan 26, 2018, 2:01 PM
Ċ Kim Border, Jan 31, 2018, 2:41 PM
Ċ Kim Border, Mar 17, 2018, 10:22 AM
Ċ Kim Border, Feb 12, 2018, 12:07 PM
Ċ Kim Border, Feb 6, 2018, 11:40 PM
Ċ Kim Border, Feb 12, 2018, 12:07 PM
Ċ Kim Border, Feb 11, 2018, 12:24 PM
Ċ Kim Border, Feb 11, 2018, 12:41 PM
Ċ Kim Border, Feb 26, 2018, 1:44 PM
Ċ Kim Border, Feb 6, 2018, 11:41 PM
Ċ Kim Border, Feb 24, 2018, 12:38 PM
Ċ Kim Border, Feb 24, 2018, 12:38 PM
Ċ Kim Border, Mar 1, 2018, 2:23 PM
Ċ Kim Border, Mar 1, 2018, 3:23 PM
Ċ Kim Border, Mar 2, 2018, 9:23 AM
Ċ Kim Border, Mar 4, 2018, 11:44 PM
Ċ Kim Border, Mar 17, 2018, 10:22 AM
Ċ Kim Border, Mar 17, 2018, 10:22 AM
SimplifiedEarthquakeCatalog2018.txt (15k) Kim Border, Feb 27, 2018, 3:52 PM
Ċ Helene Rochais, Mar 12, 2018, 12:41 PM
Ċ Helene Rochais, Mar 10, 2018, 2:33 PM
Ċ Helene Rochais, Feb 3, 2018, 3:07 PM
Ċ Helene Rochais, Feb 17, 2018, 12:59 AM
