MATH 180A: INTRODUCTION TO PROBABILITY (WINTER 2011)
For a list of some typos in the text by Durrett and in the solutions at the back, click here. You will need the login given in class to access this list.
Homework is due in the TA homework collection box by 5pm on Fridays (the TA is David Lipshutz). The homework box is on the sixth floor of AP&M and has the TA's name on it. Page references are to the course textbook by R. Durrett. Beware, a considerable number of the answers to odd problems in the back of the book are not correct. Be sure to explain your answers, do not just write down an answer or formula. You will need the login and password given in class to access solutions. These materials are copyrighted and should not be distributed without permission of Professor R. Williams.
WEEK 1:
Reading for week 1: Sections 1.1, 1.2, 1.3 of Durrett's book.
Homework for week 1, due Friday, January 7: p. 26-27 of Durrett, problems 4, 7, 9, 10, 12, 16.
Note, there is a typo in the solutions to problem 9: 57 should be 47.
Solutions to homework for week 1.

WEEK 2:
Reading for week 2: Sections 1.3 and 1.4 of Durrett's book.
Homework for week 2, due Friday, January 14: p. 27-28 of Durrett, problems 19, 20, 23, 25, 26, 31, 33 and the additional problem in the pdf file obtained by clicking here.
Solutions to homework for week 2.

WEEK 3: Reading for week 3: Sections 1.4, 1.5, 1.6 of Durrett's book.
For homework for week 3, due Friday, January 21, click here.
Solutions to homework for week 3. Note: in the solution to the last problem, the graph of the (cumulative) distribution function extends to the left of the origin at the level of the x-axis (it does not show up in the pdf version of the solutions).

Review Session: there will be a review session in AP&M 7421 at 5pm-6pm on Friday, January 21, 2011.

Extra office hour: Professor Williams will have an extra office hour at 11-11.50am on Monday, January 24.

MIDTERM, Monday, January 24, 2011, in class.
The first midterm will cover the material treated in lectures and reading assignments related to sections 1.1-1.5 of the textbook and in homework for weeks 1, 2, 3. For the midterm, please bring your student ID, a blue book or two, and pens/pencils to write with. You may bring a single 8.5"x11" sheet of paper with writing on one side of it to the exam. No books or other notes are allowed. You may bring a calculator. Make sure to justify your answers (credit will not be given for "inspired'' answers). Remember that part of each problem is to set it up and to arrive at the answer by a progression of logical steps. Please start each problem on a new page, write legibly, and put your name and section number on your blue book.
Copy of Midterm 1. Solutions to Midterm 1. Graded midterms will be available in section.

WEEK 4:
Reading for week 4: Sections 1.6, 2.1 of Durrett's book.
Homework for week 4: 50, 51, 56.
Solutions to homework for week 4.

WEEK 5:
Reading for week 5: Sections 2.1-2.4.
Homework for week 5. Chapter 2: 2, 5, 6, 9, 10, 13, 16, 21(a), 21(c), 22, 24, 27, 28, 29, 30, 35, 40, 44, 47. For problem 9: consider all possibilities (rather than "combinations") to be equally likely. Also, here licence plates have 6 characters. In problem 40, "rate 2 per minute" means "average rate of 2 per minute". Solutions to homework for week 5.

WEEK 6:
Reading for week 6: Chapter 3.
Of peripheral interest: recall the Bayes rule example about testing for spina bifida, presented in class on Wednesday of this week. On Thursday, the New York Times had an article about new developments on surgery for spina bifida.
Homework for week 6: Chapter 2, p. 76-77; problems 53, 57, 60, 68*. Chapter 3, p. 105ff., problems 3, 4, 8, 14, 19, 24, 39, 42, 59. (The starred problem is more challenging and is optional.)
Solutions to homework for week 6.

WEEK 7:
Reading for week 7: Chapter 5, Section 6.4.
Homework for week 7: Chapter 3, problems 60, 62, 64; Chapter 5, problems 2, 3, 7, 10, 13, 16, 17.
Note that for problem 64, you need to use both (a) and (b) together to determine the probabilities in the table.
Solutions to homework for week 7.

WEEK 8:
Reading for week 8: Chapter 5.
Homework for week 8: Chapter 5, problems 18, 22, 25. (You do not need to hand this homework in until Friday, March 4 -- you can hand it in with the homework for week 9.)
Solutions to homework for week 8.

The TA will hold a review session at 3-3.50pm on Thursday, February 24 in Warren Lecture Hall 2114.
Professor Williams will hold a review session at 5-6pm on Friday, February 25 in AP&M 7421.
The TA will NOT have an office hour on Friday, February 25. On Monday, February 28, Mike Gao will hold an office hour in AP&M 6452, 11am-noon (in place of the TA's office hour on the preceding Friday).

MIDTERM 2, Monday, February 28, 2011, in class.
The second midterm will cover the material treated in lectures and reading assignments related to Chapters 2, 3 and Sections 5.1, 5.2 and 6.4 of the textbook and in homework for weeks 4, 5, 6, 7. (Of course, to understand these Chapters and Sections, you will need to understand the material in Chapter 1 as well.) For the midterm, please bring your student ID, a blue book or two, and pens/pencils to write with. You may bring a single 8.5"x11" sheet of paper with writing on one side of it to the exam. No books or other notes are allowed. You may bring a calculator. Make sure to justify your answers (credit will not be given for "inspired'' answers). Remember that part of each problem is to set it up and to arrive at the answer by a progression of logical steps. Please start each problem on a new page, write legibly, and put your name and section number on your blue book. It is anticipated that graded midterms will be returned on Thursday, March 3 in Section.
For a copy of midterm 2 and solutions, click here.

WEEK 9:
Reading for week 9: Sections 6.1, 6.2.
Homework for week 9: Chapter 5, problems 27, 28, 29, 31, 36. Solutions to homework for week 9.

WEEK 10:
Reading for week 10: Sections 6.3-6.6.
Homework for week 10: Chapter 6, problems 10, 11, 16, 20, 25, 30, 33, 37, 44.
Solutions to homework for week 10.

FINAL EXAM:
The final exam will be held in WLH 2204 on Friday, March 18, 11.30am to 2.30pm. The final exam will be an overall test of the course material covered in lectures, reading assignments and homework. Please bring your student ID, a blue book or two, and pens/pencils to write with. You may bring a single 8.5"x11" sheet of paper with writing on one side of it to the exam. No books or other notes are allowed. You may bring a calculator. Make sure to justify your answers (credit will not be given for "inspired" answers). Remember that part of each problem is to set it up and to arrive at the answer by a progression of logical steps. Please start each problem on a new page, write legibly, and put your name and section number on your blue book.

Last updated December 17, 2010.