Probability Theory - Math 170A/1 - Fall 07

Writing Assignments

Homework Rules

Subject to Change

HW 10 (Due 12/7/2007)

HW 9 (Due 11/30/2007)

HW 8 (Due Wednesday, 11/21/2007)

HW 7 (Due Monday, 11/19/2007)

WARNING: HW 7 may be a little longer than usual, but you also have more time for it (due to the holidays). Do not get started too late. Try to do the problems roughly one or two days after the relevant material was given in lecture.

HW 6 (Due 11/9/2007)

HW5 (Due 11/2/2007)

• Chapter 4 Problems, page 151, Problems 13, 14, 17, 20(a)(b), 22, 25, 26, 29
• Section 4.10, page 141, Exercises (1), (2), (4)(b), (5)(a)(b)(c), (6)(a) (Use: )

HW4 (Due Monday, 10/29/2007)

• Chapter 4 Problems, page 151, Problems 1(b), 2, 3, 4, 5(a) and (b):(i)(ii) only, 6, 10, 11, 12
• Section 4.9, page 139, Exercises (4) (one method is enough), (6)

HW3 (Due 10/19/2007)

• Chapter 2 Problems, page 76, Problems 4, 7 (Hint: Carefully label all the events!), 9, 10, 16 (first paragraph only)
• Chapter 3 Problems, page 108, Problems 2, 4, 8 (You need to write more than is the answer in the back of the book!)
• An orienteer runs on the grid points (m,n) with m,n=0,1,2. She starts at (0,0), and goes to (2,2) using several steps according to the following rule: at each point in the grid she may either move up one step or to the right one step, but stay on the grid.
  (a) Find the total number of paths from (0,0) to (2,2).
  (b) Assuming that all paths are equally likely, find the probability that her path will go through (1,1).
• A fair, six sided die is rolled n times. Let A_ij be the event that the ith and jth rolls show the same number. Show that the events {A_ij : 1&lei<j&len} are pairwise independent but not independent.
• Section 3.12, page 101, (1)
• Chapter 4 Problems, page 151, Problem 1(a)

HW2 (Due 10/12^*/2007)

• Section 1.8, page 41, Exercises (1), (3), (4)
• Section 1.9, page 41, Exercises (1) (But find P(HH) any way you like), (3)
• Section 1.12., page 45, Exercises (2), (3)
• Chapter 1 Problems, page 47, Problems 6, 7, 9, 11, 13
• Chapter 2 Problems, page 76, Problems 1-3

HW1 (Due 10/5/2007)

• Chapter 1 Problems, page 47, Problems 1-4, 5 (first part only), 19, 23 (first two parts only)

HW0 (Due at 11:59pm on 9/28/2007)

Administrative:
• Read and study the syllabus and acknowledge that for the remainder of this class, you will be responsible for its content, including all policies and dates about homework and exams, even if you do not do homework assignment 0.
• Read and acknowledge items 1. through 9. above.

  Academic:

• Do your first blog assignment, due 11:59pm, 28th of September, 2007!

1. No late homework will be accepted under any circumstances.

2. You need to put the following information on top of each homework page:
   • Name
   • Class (Math 170A)
   • Lecture (1)

3. Homework must be stapled and legible.
   Clearly enumerate the problems and

   box

   or

   highlight

   your answer.

4. Assignments are to be turned in at the beginning of class and are considered semi-late if turned in between 11:10 and 11:50 on the day they are due.
   Semi-late assignments receive at most the six points for completeness (provided the assignment is complete, which is defined below in 6.), and none of the problems will be graded in detail.
   Assignments turned in after 11:50 the day they are due are considered late and hence are not accepted under any circumstances. Note that you can always turn in your assignment early.

5. Items printed in red below, are items that were changed or added.

6. Each homework assignment is worth 12 points (unless otherwise noted): six points are given for completeness (i.e. all problems have been worked out or at least attempted in earnest yields six points, one or more problems missing yields zero points) and three times two points are given for three problems (which are picked to be graded) worked out correctly.

7. The two lowest homework scores will be dropped.

8. It is crucial that you do the homework in a timely fashion, as it is essentially impossible to learn mathematics without doing a lot of problems. You may discuss homework problems with other students, the TA, or us in our respective office hours before they are turned in, as discussing problems verbally and not only thinking about them alone can be quite valuable. I do expect two things, though: (i) you should try seriously to do the exercise yourself before discussing it with anyone, and (ii) you should and in compliance with Academic Integrity rules, have to write up solutions yourself after understanding them thoroughly, without following someone else's written version. Otherwise, the homework does you no good. The point is not merely (or even primarily) to do a problem correctly, but rather to learn how to think precisely and creatively so you can go on to do more sophisticated things.

9. Homework will be returned in your discussion section. It is your responsibility to pick up your homework and report any discrepancies in the recorded score MyUCLA gradebook by the day of the final exam at the latest, by providing the relevant assignment.