2010 Summer Math 62
Introduction to Probability and Statistics
Professor Francis Su
x73616, Olin 1269, (my last name) @ math.hmc.edu
Tue, May 18 - Fri, Jun 4, Beckman B126, 8:45am and 10:30am everyday
Office Hours: Mon-Thu 3-4pm
Also, the Course Tutors will be at Platt LivingRoom:
7pm-10pm evenings before assignments are due
"Is global warming occurring? What is the state of the economy? Did
Florida's butterfly ballot swing the 2000 elections? Have the
political attitudes of college students changed over time? Has the
frequency of communication among terrorist cells increased this week?
To answer these questions in a rigorous way requires an intimate
knowledge of probability and statistics."
Prof. Paul Steinberg, HMC Humanities and Social Sciences.
Math 62 is a introduction to the basic concepts of probability
and statistics, and will equip you with tools to analyze and understand
random phenomena and experimental data in the sciences, engineering,
and the social sciences.
Probability and Statistics for Engineering and the Sciences,
Doing the reading will be essential for success in this course.
Also, the software Minitab will be used throughout this
course. It is available in the student computer labs.
Office Hours: Both I and the Course Tutors are available to
answer questions you may have. Please note the times above.
Homeworks will be due each class, and announced on the course webpage:
No late homeworks will be accepted,
but the lowest homework score will be dropped.
Please staple your HW's and write your name, course
and section number, assignment number, and due date on your HW.
Also, how you communicate mathematics is just as important as
See these department
guidelines for formatting homework and also this handout on mathematical
writing. The graders can take off points for work
that is not clearly explained or written neatly and in
There will be a daily quiz, which may cover material from either the
lecture, reading, or the homework.
Your homework average and quiz average will each count 1/2 of your
course grade. Lowest quiz and lowest homework
scores will be dropped.
All are expected to abide by the HMC honor code.
Cooperation on homework is encouraged in this class, but be sure to
write up all solutions individually
and be sure to credit any collaborators.
Basic Probability and Counting (2.1-2.3)
| HW 1 due
Conditional Probability and Independence (2.4-2.5, 3.1-3.2)
| HW 2 due
Discrete Random Variables, Expected Values/Variance
| HW 3 due
A Catalog of Discrete Distributions
Continuous Random Variables, Exponential Dist. (4.1-4.2, 4.4)
| HW 4 due
Normal Distribution, Joint Distributions(4.3, 5.1)
| HW 5 due
Covariance, Correlation (5.2)
| HW 6 due
Random Samples and Statistics (5.3-5.5)
Point Estimation (6.1-6.2)
| HW 7 due
Estimators, Standard Error (6.1)
Confidence Intervals (7.1-7.3)
| HW 8 due
Hypotheses Tests (8.1-8.3)
| HW 9 due
p-values, statistical significance (8.4-8.5)
| HW 10 due
Linear Regression (12.1-12.2),
|HW #1 (due Wed Week 1)
||READ 2.1-2.5 and this handout.
DO Chapter 2 ( 8, 18, 31, 35, 44 )
Problem W. In no more than two sentences, explain why good
mathematical communication is important, and comment on whether the
writing in textbooks from any of your core courses follow the guidelines
in the handout.
Problem A. Get in a group of 3-4 people and pick ONE of the
following questions to discuss. What data would you need, what methods
would you use, how could you estimate your likelihood of being
correct in your conclusion? Write a paragraph about your discussion
(write up your thoughts individually, but be sure to say who
was in your discussion group).
1. You see a pattern of black and white tiles in a 100x100 square grid
in your bathroom. Is the pattern truly random? Devise a test.
2. Do basketball players really experience "streaks", in which they
appear to have a "hot hand": a period of time when the percentage of
shots they make is unusually high? Or is their performance adequately
explained by random luck? Devise a test to distinguish the two.
3. Based on gene sequencing, molecular biologists often attempt to
develop a "phylogenetic tree" that describes the evolutionary
relationships between species. Unfortunately, using different parts
of the genome can sometimes lead to many different trees. Unlike
numbers, you can't just "average" all these trees... or can you? Is
there a good notion of "average" for trees?
|HW #2 (due Thu Week 1)
DO Chapter 2 ( 56, 62, 82, 88 ) Chapter 3 ( 10, 12 )
On problem 3.10b, interpret "difference" to mean "absolute
difference". The problems from chapter 3 are to encourage you to do
|HW #3 (due Fri Week 1)
||READ 3.4-3.6 and READ 4.1
DO Chapter 3 ( 16, 29, 31, 43, 48cde )
|no HW due Mon Week 2
except the reading
|READ 4.2-4.4, SKIM 4.5
no written HW. Review the material for Monday's quiz.
|HW #4 (due Tue Week 2)
Skim, but do not do, the problems in Section 3.4. Familiarize
yourself with examples where the binomial distribution is useful.
Do Chapter 3 ( 74, 75abd, 80, 84 ) Chapter 4 ( 8, 20 ).
|HW #5 (due Wed Week 2)
Do Chapter 4 ( 32, 46, 60, 98, 100 )
|HW #6 (due Thu Week 2)
||READ 1.1-1.4 AND 5.3-5.4
Do Chapter 4 ( 53a ) Chapter 5 (10, 12, 14, 24, 30 )
|HW #7 (due Fri Week 2)
||READ 5.5, 6.1
DO Chapter 1 ( 44, 68 ) Chapter 5 ( 37, 42 ) and the Minitab Tutorials:
1: Intro to Minitab
Tutorial 2: Sampling Distributions
Note that in Tutorial 1, there is nothing to hand in--- just
examples to try. You'll need your book to refer to the exercises in
the tutorial. You might also
want to download the data sets for the book
.zip format. Do enough of the suggested exercises in the
tutorial to ensure you understand
how to use Minitab. (Ignore problem 1-34, and problem 1-47 has no
dataset in the .zip file.)
To get credit for Tutorial 1,
please record on your HW sheet whether or not you
actually followed the Tutorial.
In Tutorial 2, note there is something to hand in.
Minitab is available in all the PC labs on campus.
|HW #8 (due Tue Week 3)
Do Chapter 5 ( 50, 55, 90 ) Chapter 6 ( 10, 19 ) Chapter 7 ( 14, 23 )
|HW #9 (due Wed Week 3)
||SKIM 7.4 and READ 8.1-8.5
Do Chapter 7 ( 32 ) Chapter 8 ( 7, 10, 18abc, 32a ).
|HW #10 (due Thu Week 3)
||READ 9.1-9.2, SKIM 9.3-9.5, READ 12.1-12.5
Do Chapter 8 ( 41, 54 ) Chapter 9 ( 5abc, 28 )
For Minitab help, see these tutorials
(you don't have to do the assignments in them):
3: Hypothesis Testing
4: Linear Regression.
REVIEW AND STUDY FOR THE FINAL QUIZ
It's worth 4 quiz scores.
- You may prepare a one-page sheet of
notes, double-sided, for use during this quiz.
Since the point of this is to help you review,
this must be prepared by you (you may not copy someone else's).
- Use calculators, but only four-function, square root
operations will be allowed (you can't use the other functions).
- I will provide any tables that you might need.
- The quiz will be a take-home, available
Thursday and due Friday afternoon at 4pm in Math Department Front
Office, Olin 1260..