Homework for Math 191
HW 1: Due Tuesday Sept 24:
- Read Sections I, II(1-5).
- Problems from Feller Vol 1: I.8 #5, 6, 9, 18, 19; II.10: #10, 15, 19, 21; II.11 #3, 4.
HW 2: Due Tuesday Oct 1:
- Read Sections II(5-9), III(1-6).
- Problems from Feller Vol 1:
I.8 II.10: #35, 36; II.11 #20,21,22; III.10: #1,2,3,4,7.
HW 3: Due Tuesday Oct 8:
- Read Sections III(7-10), IV, VII(1-2).
- Problems from Feller Vol 1:
III.10: #6, 9,10, 14; IV.6: #4, 11; VII.7: #1, 5, 7.
- Note that for the last two problems, you can view them
as a random walk.
HW 4: Due Tuesday Oct 15:
- Read Sections V(1-4), VI(1-6)
- Problems from Feller V.8 #2,6,13,21,26; VI.10: #3,7,12,15,18.
HW 5: Due Tuesday Oct 22:
- Read Sections VI(7-8), VII.
- Problems from Feller: VI.10: 23, 24. VII.7: #2, 3, 4, 9, 11, 12, 18.
HW 6: Due Tuesday Oct 29:
- Read Sections VIII(1,3-4), IX.
- Problems from Feller: VIII.7: #4,5; IX.9: #2,8,9,10,19,26.
Note: There will be no HW due Nov 5.
HW 7: Due Tuesday Nov 12:
- Read Sections X, XI 1-4, XIII 1-2.
- Problems from Feller: IX.9: #32; X.8: #1, 2, 14, 15, 16, 17;
XI.7: #3, 7, 15.
HW 8: Due Tuesday Nov 19:
- Read Sections XII 1; XIII 1-7;
- Problems from Feller: Vol 1: XI: #9(a); XII:#2; XIII: #1 (Prove Thm 3 only), 4, 11.
- Vol 2: I: #1, 2.
HW 9: Due Tuesday Nov 26:
- Read Sections Vol 2: 1;
- Misc. Problem: Suppose that U is a function from [0, inf) to
[0,1] which satisfies U(s + t) = U(s) U(t) for all s,t in [0, inf).
Suppose also that U(s) is nonzero for some s > 0 and that U is not
constant. Prove that U(s) = e^(-as) for some a > 0.
- Problems from Feller: Vol 2: I: #4(i), 7, 10, 16, 20, 37.
Note:There will be no HW due on Dec 3.
HW 10: Due Tuesday Dec 10:
HW 11: Due Tuesday Dec 17: