# 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,