# STA 6466: Assignments

- Assignment 1 (Due Sep 2): Billingsley, exercises
2.4, 2.8, 2.9, 2.11.
- Assignment 2 (Due Sep 9): Billingsley, exercises
2.13, 2.17, 3.11, 3.12, 10.2. (Note: Exercise 3.11(b) proves that
the old lambda–system postulates are equivalent to the new
lambda–system postulates, and exercise 3.12(a) is just a restatement
of the pi–lambda theorem and has already been discussed in class.)
- Assignment 3 (Due Sep 16): Billingsley, exercises 2.5(b),
12.1 (only for the case of measures on the real line; do NOT do
the extension to k–dimensional Euclidean space). Hint: On 12.1, you
may wish to use Cauchy's equation from Appendix A20 of
Billingsley.
- Assignment 4 (Due Sep 23): Billingsley, exercises 12.9,
12.11. Note: Part of 12.11 is wrong. Try to find the problem and
fix it.
- Assignment 5 (Due Sep 30): Billingsley, exercises 13.1,
13.8.
- Assignment 6 (Due Oct 7): Billingsley, exercises 13.9, 13.10.
- Assignment 7 (Due Oct 14): Billingsley, exercises 16.1, 16.4,
16.8, 17.5, 17.6. (Note: In 16.4, you must assume not only that a_n
and b_n are integrable, but also that the functions a and b are
integrable. Otherwise the result can fail.)
- Assignment 8 (Due Nov 4): Billingsley, exercises 17.7 and 32.6.
- Assignment 9 (Due Nov 18): Billingsley, exercises 18.2, 18.4,
18.13, 32.5, and the problem given here.
- Assignment 10(Due Dec 7).

There are many other interesting exercises in Billingsley. Some you
may wish to try are given below. I will add to this list as we go
along.
- 2.3, 2.4, 2.5, 2.7, 2.8, 2.9, 2.10, 2.11, 2.12, 2.13, 2.16, 2.17, 2.19
- 3.3, 3.11, 3.12
- 10.1, 10.2, 10.3
- 12.1, 12.9, 12.11
- 13.1, 13.6, 13.8, 13.9, 13.10, 13.11, 13.14
- 14.8(a)
- 16.1, 16.2, 16.4, 16.8
- 17.4, 17.5, 17.6, 17.7, 17.8
- 18.1, 18.2, 18.3, 18.4, 18.8, 18.9, 18.11, 18.14
- 19.1
- 20.20, 20.22, 20.24
- 21.7, 21.8, 21.9, 21.21
- 32.5, 32.6,