HOMEWORK

Homework is from the textbook by Resnick. Homework is due in class on Wednesdays. Please hand in the starred problems.

Homework 1: due Wednesday, October 6, 2010, in class.
Chapter 1: 9, 12*, 14, 15, 16, 17*, 19, 25*, 31, 34.
Re Problem 25: there is a bad typo in this problem. It should say that script A is the collection of finite disjoint unions of arcs for theta lying in intervals of the form [a,b) with rational endpoints.
Solutions to starred problems for Homework 1. You will need the login and password given in class to access these solutions.

Homework 2: due Wednesday, October 13, 2010, in class.
Chapter 2: *1, 3, 5* (note that A should be A_epsilon there), 6, 8, 11*, 16.
Re problem 1: the definition of P is only relevant for parts (b) and (c).
For problem 11, you can assume that P is a probability measure.
Solutions to starred problems for Homework 2.

Homework 3, click here. Due Wednesday, October 27, 2010. Note that for problem 5 from Chapter 3 of Resnick, you may assume that X is a random variable.
Solutions to starred problems for Homework 3.

Homework 4: due Wednesday, November 3, 2010, in class.
Chapter 3: 6, 7*, 11, 12, 14, 15*, 20*, 22.
Note: there is a typo in problem 20 --- the potential range of X_tau should be the whole real line.
Hint for 20: You can approximate tau by a sequence of random variables {tau_n} where tau_n takes only dyadic rational values. For example, tau_n = (k+1)/2^n on { w: k/2^n <= tau(w) < (k+1)/2^n}. Use this together with the continuity of X as a function of time to approximate X_tau by a sequence of random variables X_{tau_n}.
Solutions to starred problems for Homework 4.

Homework 5: due Wednesday, November 10, 2010, in class.
Chapter 4: 3, 5, 6, 8, 9*, 13*, 16, 17(a,b)*, 18, 20*.
Hint for problem 9: recall that int_x^1 1/u du = - log x for 0 < x < 1 and use upper and lower bounds for the integral. For problem 13, assume that 0 < p < 1.
Solutions to starred problems for Homework 5.

Homework 6: due Wednesday, November 24, 2010, in class. (You can also give the homework to the TA sometime before class.)
Chapter 5: 4, 6*, 7, 11*, 13*, 29.
Solutions to starred problems for Homework 6.

MIDTERM: For a copy of the midterm, click here. For a copy of the midterm solutions, click here.

Homework 7: due Friday, December 3, 2010, 5pm in the TA mail box on the 6th floor - Michael Kelly, Math 102.
Chapter 5: 16(a,b*,c*): 16(a) was part of a previous homework (HW 4, 15) and you don't need to do it again if you did it before; 20, 30, 31, 32, 34, 36*, 40.
Chapter 6: 2*: for this problem you may use some version of the strong law of large numbers from Chapter 7.
Solutions to starred problems for Homework 7.