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

Overview: "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.

Text: Jay Devore, Probability and Statistics for Engineering and the Sciences, 7th edition. 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: Homeworks will be due each class, and announced on the course webpage: http://www.math.hmc.edu/~su/math62/. 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 solving problems. 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 complete sentences.

Daily Quizzes: There will be a daily quiz, which may cover material from either the lecture, reading, or the homework.

Grading policy: Your homework average and quiz average will each count 1/2 of your course grade. Lowest quiz and lowest homework scores will be dropped.

Honor Code: 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.

Calendar

MonTueWedThuFri
Week 1

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 (3.3-3.6)

HW 3 due

A Catalog of Discrete Distributions

Week 2

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)

Week 3

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),

 

Final Quiz

HW Assignments
HW #1 (due Wed Week 1) READ 2.1-2.5 and this handout.
DO Chapter 2 ( 8, 18, 31, 35, 44 ) and

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) READ 3.1-3.3
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 the reading!

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) READ 5.1-5.2
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) READ 5.1-5.2
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:
Tutorial 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 here in .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) READ 7.1-7.3
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):
Tutorial 3: Hypothesis Testing
Tutorial 4: Linear Regression.

REVIEW AND STUDY FOR THE FINAL QUIZ
It's worth 4 quiz scores.

Notes:

  • 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..