Please spend at least 2 hours a night reading the material/looking at the proofs/making sure you understand the details. Below is a tentative reading list and homework assignments. It is subject to changes depending on the amount of material covered each week. I strongly encourage you to skim the reading before class, so you are familiar with the definitions, concepts, and the statements of the material we'll cover that day. Also, you can frequently do the homework well before it is due -- you are urged to start working on the problems as soon as you can.

First Unit: Introduction (The Birthday Problem, Roulette, Basics of Probability)

• Week 1: September 5 to 9
  • Homework: Due Thursday, September 15: (1) If you have 100 days in the year, how many people do you need in a room for there to be at least a 50% chance that two share a birthday? (2) Generalize the argument from class of 20 blocks of 5 to blocks of size 6 (I can do 10 of size 10 without too much work). Note we still have 100 spins, and each spin has a 50% chance of being red, 50% chance of being black.
  • Extra Credit: Due Thursday, September 15: Use the results from Schilling's paper to estimate how long you can play before it is very likely that you have at least one consecutive run of 5 black spins in roulette.
    
• Week 2: September 12 to 16
  • Read: Chapter 1: Sections 1.1 (skip all material on odds and gambling), 1.2, 1.3, 1.4.
  • Homework: Due Tuesday, September 20: Section 1.1: Page 9: #3, #5, #7. Section 1.3: Page 30: #3, #10. Also prove if A is a subset of B then Prob(A) is at most Prob(B).
  • Extra Credit: Due Tuesday, September 20: Section 1.3: Page 30: #13, #16a.
• Week 3: September 19 to 23
  • Read: Sections 1.4, 1.5 (just read the box on page 49 and example 3 on page 50), 1.6, 2.1, 3.1.
  • Homework: Due Tuesday, September 27: Section 1.4: #1, #3, #9. Section 1.6: #5, #6.
  • Extra Credit: Also prove or disprove that if A, B and C are pairwise inidependent then A, B and C are independent.
• Week 4: September 26 to 30
  • Read: Sections 3.1, 3.2, 3.3, 3.4.
  • HW: Due Thursday, October 13: Section 2.1, Page 91: #2 (just the first part, not the relative frequencies), #7, #10. Section 3.1, Page 158: #3, #10, #16b (but look at #16a). Also do: If X is uniform on [-1,1], find the probability density function of Y if Y = X^2. [[HW moved back b/c TA was sick, then Mountain Day, then Fall Break.]]
• Week 5: Oct 3 to 7 (no class on Thursday Oct 6 due to Mountain Day)
  • Read: Sections 3.2, 3.3, 3.4.
  • HW: Due Tuesday October 18: Section 3.2, Page 182: #1, #4, #7, #10, #11 (don't do the simple upper bound), #13ad. [[HW moved back b/c of Mountain Day.]]
  • Extra Credit: Section 3.2, Page 183: #13bf, #15 (econ oriented).
• Week 6: Oct 10 to 14 (no class on Tuesday Oct 11 due to Fall Break)
  • Read: Sections 3.3, 3.4.
  • HW: Due Thursday, October 20: Page 202: #2, #3abcd, #12, #14, #27.
• Week 7: Oct 17 to 21
• Read: Sections 3.3, 3.4.
• HW: Due Thursday, October 27: Section 3.4, Page 217: #1abc, #7abcd, #10abc (hard). Section 3.5, Page 234: #4 (hint: first find the probability of at least five misprints on any one page). Section 4.4, Page 310: #9a.
• Week 8: Oct 24 to 28
• Read: Chapters 13 and 14, including sum of Poisson Random Variables.
• Homework: Midterm due Tuesday, November 1st at the start of class, so no written HW.
• Week 9: Oct 31 to Nov 4: No class on Thursday due to power outage, use as extra time for the exam
• Read: Chapters 13, 14, including sum of Poisson Random Variables.
• Homework: Midterm due Thursday, November 4th.
• Week 10: November 7 to 11: No class on Friday because of (Optional) Midterm II
• Read: ChiSquare chapter of my book (notes provided in class) and the Method of Least Squares notes.
• Least squares handout for the lecture.
• Homework: Due Thursday, November 17: Section 5.3: #3a. Also do (1) Calculate the probability a chi-square distribution with 2 degrees of freedom is at least twice as large as its mean (so if the mean is mu, we want the probability it is 2mu or greater). Problems from my handout on Method of Least Squares notes: Page 9, #3.3, Page 10, #3.9.
• Optional midterm is due at the start of class on Tuesday, November 15.
• Week 11: November 14 to 18:
• Read: ChiSquare chapter of my book (notes provided in class)
• Homework: Due Thursday, November 17: Section 5.3: #3a. Also do (1) Calculate the probability a chi-square distribution with 2 degrees of freedom is at least twice as large as its mean (so if the mean is mu, we want the probability it is 2mu or greater). Problems from my handout on Method of Least Squares notes: Page 9, #3.3, Page 10, #3.9.

Do the first few final exam problems by the start of class on Friday, December 2nd; no class on Thursday to have extra time.