MATH 180A: INTRODUCTION TO PROBABILITY (WINTER 2009)
Homework is due in the TA homework collection box by 5pm on Fridays. The homework box is on the sixth floor of AP&M and has the TAs name on it: Allison Cuttler. Page references are to the course textbook by S. Ross. 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: read Chapter 2 (except 2.5).
Homework for week 1, due Friday, January 9: P. 55: 1, 5, 11, 14, 23. P.61: 11.
Solutions to homework for week 1.

WEEK 2:
Reading for week 2: read Chapter 1 (except 1.6), read Section 2.5.
Homework for week 2, due Friday, January 16:
p. 16: 1, 5, 8(b), 15, 20, 27, 30; p. 58: 30, 39, 41, 53.
Extra homework problem: suppose a fair coin is tossed infinitely many times. You can represent an (arbitrary) outcome of this experiment as an infinite sequence (x1, x2, .....) where each xi is either H or T. For each positive integer n, consider the event A(n) that the first n tosses yield heads. What is the probability of A(n)? (Hint: it is the reciprocal of the number of possible outcomes for the first n coin tosses.) Let A be the event that all of the tosses yield heads. What is the relationship between A and the A(n)? By using the continuity of probability, find the probability of the event A.
Solutions to homework for week 2.

WEEK 3:
Reading for week 3: read Chapter 3.
Homework for week 3, due Friday, January 23, 2009:
p. 111: 1, 12, 16, 20, 32, 42, 50; p. 124: 2.
Solutions to homework for week 3.

First Midterm. Monday, January 26, 2009.
Midterm and solutions.

WEEK 4:
Finish off Chapter 3, start Chapter 4.
Homework for week 4, due Friday January 30, 2009:
p. 118: 54, 57, 62, 64, 66; p. 187: 1, 12.

Solutions to homework for week 4.

WEEK 5:
Finish off Chapter 4, start Chapter 5.
Homework for week 5, due Friday February 6, 2009:
P. 187: 17, 23, 25, 32, 38, 49, 57, 65, 68. (Note that the answer to 68 is wrong in some copies of the text: the power should be 10 not 80).
Solutions to homework for week 5.

WEEK 6:
Finish Chapter 5, start Chapter 6.
The following homework is due on Friday February 13, 2009.
Extra homework problem (NOT optional). Consider a geometric random variable X with parameter p.
(a) Find an expression for the probability that X is (strictly) greater than n, for n=0, 1, 2, ...
(b) Prove that X is memoryless, i.e., prove that P(X>n+m|X>n) = P(X>m) for n= 0, 1, 2, ..., m=0, 1, 2, ...
Problems from the text. p. 247: 1, 4, 6, 13, 15(a), (b), 18, 22, 28, 31, 32.
Solutions to homework for week 6.

WEEK 7:
Reading: Chapter 6 up to p. 288.
Homework for week 7 due Friday, February 20, 2009:
p. 313: 1, 6, 8, 9, 13, 20, 22.
Solutions to homework for week 7.
Note: the second midterm is on Monday, February 23rd. See the main webpage for details.

MIDTERM 2: Copy of exam and solutions.

WEEK 8:
Reading: Finish Chapter 6 up to page 296.
Homework for week 8 due Friday, February 27, 2009:
p. 316: 24, 27, 33. (Short homework this week due to the midterm on Monday.)
Solutions to homework for week 8.

WEEK 9:
Reading: Chapter 7.
Sheet on Kurtosis.
Homework for week 9 due Friday, March 6, 2009:
p. 408; 5, 6, 8, 16, 30, 33, 38, 45(a), 75(c).
Solutions to homework for week 9.

WEEK 10:
Reading: Chapter 8.
Homework for Week 10, due Friday, March 13, 2009: Chapter 8, 2, 7, 15.
Solutions to homework for week 10.
TA addendum to discussion in review session on Friday, March 13.

Last updated February 9, 2009.