The following information is available concerning Stat 515H,
Fall 2015, MWF 11:15 a.m. –12:05 p.m.
 General information
 Course syllabus
 Homework assignments
 Examinations
 Hour exam #1 is scheduled for
Wednesday, October 21, 2015 from 11:15 a.m. until 12:05 p.m. in LGRT 173.
 The exam will cover introductory material and Chapters 1, 2, and 3, focusing on the material
covered in class and in homework assignments #1, #2, #3, and #4.
 A document outlining the material to
review for the exam is available online.
 Hour exam #2 is scheduled for
Wednesday, November 18, 2015 from 11:15 a.m. until 12:05 p.m. in LGRT 173.
 The exam will cover Chapter 4 and Chapter 5, focusing on the material
covered in class and in homework assignments #5, #6, and #7.
 A document outlining the material to
review for the exam is available online.
 The final exam is scheduled for ...
 Other material (page numbers in these documents
refer to the 7th edition of the text, except for item #9, which refers
to the 9th edition)
 Definitions of "random" and
"chance."

Review of the book
Beyond Coincidence: Amazing Stories of Coincidence and the Mystery
and Mathematics Behind Them from The New York Times online.
This review mentions the birthday problem.

Review of the book
The Drunkard's Walk: How Randomness Rules Our Lives from The New York Times online.
 Review of the book
Rolling the Bones: The History of
Gambling from The New York Times online.
 Hints
for solving the hotel coincidence problem, which is problem #4 in
homework 1.
 Illustrating
Stirling's formula.
 Proof of Stirling's formula.
Except for the statement of Stirling's formula, you are not
responsible for this material. However, because this is an honor
course, I would be happy to help anyone in the class who would
like to understand the details of this proof.
 Statement and proof of De Morgan's
laws. For a more general formulation, see
http://planetmath.org/encyclopedia/DeMorgansLaws.html.
 Problem re 3
languages  p49, #12.
 Probabilities of 5card poker hands.
This is taken from
http://www.math.hawaii.edu/~ramsey/Probability/PokerHands.html.
 Review of a book on Bayes's Formula from The New York Times online:
The Theory That Would Not Die: How Bayes' Rule Cracked the Enigma Code, Hunted Down Rusian Submarines
and Emerged Triumphant from Two Centuries of Controversy. This
excellent review clearly explains Bayes's Formula. Try to do the
problem involving the three coins, for which the answer is 4/5.
 Comments on independent events.
 Analysis of the game of craps.
The probability of winning is 244/495 = 0.492929.
Because this in an honors course, I would like everyone in the class
to understand the details of this calculation.
 Discrete random variables
 Facts about E[X] and Var(X).
 Weak law of large numbers for
fair coin tossing.
 Law of large numbers for
i.i.d. random variables.
 Constructing binomial random
variables.
 Poisson limit theorems and Poisson
approximation. Two videos that discuss the proof of Theorem 1
on this handout are available online:
video #1 and
video #2.
 The birthday problem,
exponential approximation, and Poisson approximation.
 Preliminaries concerning normal random variables.
 Normal random variables.
 Table 5.1. Area Φ(x) under
the standard normal curve to the left of x.
 P(X \in
Interval) for Continuous Random Variables X.
 Interpolating Φ(x) for 0 < x < 3.49
not in Table 5.1.
 The normal
approximation to the binomial distribution.
 Central limit theorem. Enter "central limit theorem" in
Google
and visit several websites that illustrate this remarkable theorem.
 Law of large numbers, normal approximation, and
Stirling's formula.
 Sums of independent random variables
via convolutions and moment generating functions.
 The sum of independent normal
random variables is normal.
 Facts about E[X] and Var(X)–#2.
 An unbiased estimator of the
variance of i.i.d. random variables.