Homework for STA 2111F (Fall, 1997) -- tentative
All homework questions are taken from the textbook, "Probability and
Measure", 3rd ed., by Patrick Billingsley.
(The questions are found at the end of the corresponding section; for
example, question 2.4 is the fourth question at the end of section 2.)
Note that some questions have hints provided, on pages 552-580 of the
These questions are tentative, and modifications may be
announced during lectures.
Students may discuss solutions to the homework questions, especially
when they are stuck, but they should understand them and write them up
entirely on their own. Direct copying is strictly forbidden!
Each homework is due by 4:00 p.m. on the day indicated, and should be
placed in my mailbox (in Sid Smith 6021) or slid under my office door
(Sid Smith 6024) by that time. Extensions will be considered, but only
when discussed well in advance.
Homework #1, due Friday October 10, 4:00 p.m.
Include your name, department and year, e-mail address and/or phone
number, and any comments you have about the course.
Text questions: 1.1, 2.3, 2.4, 2.13, 3.5, 4.2(a), 4.4, 4.6
For question 2.13(c), note the formal definition of countable additivity
on a field, e.g. item (iii) on page 160.
For question 3.5, recall the definition of inner measure from
Homework #2, due Friday November 7, 4:00 p.m.
Text questions: 5.3, 5.4, 5.5, 5.13, 6.11, 22.1, 22.5(a), 22.6
For question 5.5, recall that
an inequality is sharp if it sometimes holds with equality.
Question 5.13 is not clearly worded; you
may take the question to be, "Prove the inclusion-exclusion formula".
For question 6.11, the convergence should
be shown with probability 1.
For question 22.1, you may assume that the X_i are indicator
random variables, i.e. they only take the values 0 and 1. But Y is an
arbitrary random variable.
Homework #3, due Thursday December 4, 4:00 p.m.
Text questions: 15.2, 17.7, 7.1, 7.7, 8.3, 8.13, 8.20, 22.8
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