Math 157
Probability
Spring 2012

Professor Francis Su
x73616, mylastname @ math.hmc.edu
Office Hours: TUE 3:30 - 4:30pm or by appointment.

Course Content: This course builds on Math 62 (Intro to Probability and Statistics) by covering core concepts of probability in greater depth, as well as additional topics, with attention paid to proofs and simulation.

Text: Grinstead and Snell, Introduction to Probability, 2003. It is available in book form as well as an online pdf. The website for the book is here. You will note there are 2 versions of the book there; we will be using this one because it matches the printed book. Doing the reading will be essential for success in this course.

Prerequisite: Math 35 (Intro to Probability and Statistics).

Homeworks: Homeworks, assigned weekly, due in class on Thursdays, will be announced on the course webpage: http://www.math.hmc.edu/~su/math157/

Grading policy: Two midterms, and homework each worth 30%, the highest component worth 40%.

Honor Code: All are expected to abide by the HMC honor code. Cooperation is ENCOURAGED in this class, but write up all solutions individually and be sure to credit any collaborators.

HW Assignments
HW #1 (due 1/19) READ all of Chapter 1.
DO 1.1 ( 3, 4, 9, 14 )

(This is a shorter first week homework.) Please read these guidelines on writing mathematics well. For simulations, if you don't like to write your own code, you might consider using a spreadsheet which often have built-in functions. Please report on the results of your simulations, and what platform you used (no need to include code).

HW #2 (due 1/26) READ all of Chapter 2 and skim Chapter 3.
DO 1.2 ( 10, 14, 15, 17, 22 ) 2.1 ( 5, 6, 9 ) 2.2 ( 5bc, 14 )

Hint on 1.2.15: what is the sample space for this experiment?

HW #3 (due 2/2) READ Chapter 4 and skim Chapter 5.
DO 2.1 ( R10 ) 2.2 ( R6, 8acfg, 11, 12 ) 3.1 ( 9 ) 4.1 ( 1, R5, R16, 20 ) 4.2 ( 2, 8, 11, 12 )

"R" means READ but do not do the problem.
Notes: on 2.2.8, draw a good picture.

Midterm (Part I, Part II to be available Monday. Watch the class e-mail list) (due 2/9) Part I is open-book, open-notes, open-any source, but you may not collaborate with others.

Problem A. In this problem, you will review common distributions. Make a table with each of these 10 distributions along with their: (i) parameter definitions (ii) distribution/density function (iii) mean, (iv) variance, and (iv) an example of random variable with that particular distribution:

    binomial, geometric, Poisson, negative binomial, hypergeometric, uniform, exponential, beta, normal, chi-squared.

AND DO 5.1 ( R23, 24, R26, R32, 45 ) 5.2 ( 2, 34 )

"R" means READ but do not do the problem.

You may wish to prepare a note-sheet for Part II.

HW #4 (due 2/16) REVIEW Chapter 6 and READ Chapter 7 and 8.
DO 6.1 ( 6, R12, 14, R21, R22, 25abc ) 6.2 ( 10, 17, R18 ) 6.3 ( 3, 7 ) 7.1 ( 2, R9 ) 7.2 ( R1, 5b, R6, 10 )

"R" means READ but do not do the problem.

HW #5 (due 2/23) READ Chapters 9 and 10
DO 7.1 ( R7 ) 8.1 ( R4, 6, 7, R14 ) 8.2 ( 1, 2, R8a ) 9.1 ( 8 ) 9.2 ( 1, 9 ) 9.3 ( 4, 13 ) 10.1 ( 1acef )

"R" means READ but do not do the problem.

2nd Midterm (Part I, Part II to be available Wednesday. Watch the class e-mail list) (due Tue 3/6) Part I is open-book, open-notes, open-any source, but you may not collaborate with others.

DO 8.1 ( R14 ) 9.2 ( 4 ) 9.3 ( 2 ) 10.1 ( 8 ) 10.3 ( 1ac, 2ac )

You should do Part I before doing Part II. You may wish to prepare a note-sheet for Part II.

"R" means READ but do not do the problem.