ANNOUNCEMENTS

Midterm 2 will be held Tuesday, Oct 6, in our classroom: WEH 7500, at the usual class time. The exam will start at 2 p.m. promptly, so please don't be late.
Review Session for Midterm 2 will be held in WEH 7500 from 12 p.m. - 2 p.m. on Sunday, Oct 4. This will be TA led. A handout for the review session (containing new practice problems) will be posted on Canvas by Saturday at noon.
Extra Monday (Oct 5) Office Hours There will be the usual office hours on Monday with Nikhil from 2:30 - 4 and with Megha from 5 - 6:30. Those office hours are meant to get help with questions from the Review Session as well as general questions. In addition, Mor will hold extra office hours to go over any extra problems that you may have done in preparing for the exam. Mor's office hours will be 1:30 p.m. - 2:30 p.m. as well as 6:30 p.m. - 7:30 p.m. on Monday.
What Midterm 2 covers: Chapters 5-7, plus a touch of Chapter 8.
- Regarding Chapter 8: We know that you have not done homework yet on Chapter 8, so we will keep that material easy and stick to only what was covered in class.
- Regarding Chapters 5-7: The level of the problems is similar to your homework, where some problems are very quick and others require some thinking.
- You are responsible for everything in the book in Chapters 5-7, EXCEPT for Section 5.6 on Covariance, which we skipped over, and Section 6.7 on Recurrence Relations.
- Since this course is cumulative, you should make sure you still know the material in Chpts 1-4, although the focus will be Chpts 5-7.
What you can bring to Midterm 2: Midterm 2 is closed book, closed notes, closed calculators, etc. The only thing you're allowed is one 3x5 index card with writing on 1 side.
Tips for studying for Midterm 2:
- When reading your book, cover up all the answers and write them down yourself with pen and paper. There are a lot of good examples in the book.
- On Saturday, the TAs will post a handout for Sunday's Review Session. This will include a bunch of new practice problems. Fill out the entire handout before you go to the Sunday review.
- Go over all the homework problems again, but check your solution against the class solution that we handed out. The class solution often contains some nice simplification tricks.
- Go over your recitation handouts and try all the problems yourself again. If you can't do some of these, contact your TAs or bring your questions to the Review Session.
- Go over your class handouts and fill them in yourself. If you have questions, see Mor or Feras.
- Doing extra problems in the book is always a great idea. We will not be releasing solutions to these problems, however you can ask us to check if your answer is correct.
Where to go to get materials:
- Homework solutions are available in the *bins* outside Mor's door -- GHC 7207.
- Index cards are available outside Mor's door -- GHC 7207.
- Handouts from class and recitation are available on Canvas.
- If you missed a class, or just didn't take good notes, you can get filled-in handouts directly from the instructors.
- The Review Session handout will be available on Canvas by Saturday morning.
Tips for what you might want to write on your index card:
- For every distribution we've studied, you want to make sure you know the mean, variance, p.m.f. or p.d.f., tail, z-transform.
- Major theorems and definitions.
- It's useful to have a list of approaches you can apply to solve problems if you're drawing a blank, e.g. use conditioning, use linearity, etc.

HOMEWORK

Homework will go out each week on Friday. When the homework goes out, you already have all the material you need to do it that day. Homework will be due each week the following Friday at 12:50 pm sharp. It must be uploaded to Gradescope. Please upload EARLY. This is your one chance to get practice with doing problems to prepare for exams. Please do not use LLMs and start right away! You must get the homework in on time because we give out solutions during recitation. There are no late days (not even late minutes). However we will drop your 1 lowest homework score at the end of the class. Please save up your drop for when you're sick or traveling. Homework is graded within a couple days. You can submit a regrade request on Gradescope (including a detailed explanation of why you think you were misgraded) within 2 days of when you get your homework grade.

Here is an OPTIONAL Latex Template template.tex. You are also free to hand-write your homeworks, provided you can keep your handwriting readable.
[HW 1: Review of prerequisites] 1.1, 1.2, 1.4, 1.5, 1.6, 1.7 in the Exercises Section of your PnC textbook, plus 1.11, 1.12, 1.14 in this pdf file. Please read the instructions in the pdf file. Due 12:50 pm on 8/28.
- For Exercise 1.5, the Taylor series expansion should be around the point 0.
[HW 2: Events] 2.7, 2.9, 2.10, 2.11, 2.12, 2.16, 2.22, 2.25, 2.28 in PnC textbook. Due 12:50 pm on 9/4.
- For Problem 2.22 (Monty Hall), we recommend that you take the following steps.
  (1) Since the contestant knows nothing, assume WLOG that the contestant picks door 1.
  (2) Let D be a r.v. representing the door that has a car behind it.
  (3) Let Y be a r.v. representing the action of the game host.
  (4) You are trying to compare P{D= 1 | Y = i} with P{D = 2 | Y= i} or P{D = 3 | Y= i} for all possible values i. Explain what this means in terms of switching. Now derive each.
[HW 3: Discrete R.V.s and expectation] 3.8, 3.10, 3.12, 4.4, 4.5, 4.10, 4.13, 4.15, 4.16, 4.18. Due 12:50 on 9/11.
- Problem 4.5, assume that birthdays are equally likely to fall on any day.
- Problem 3.12: Each sub-question asks if Y_1 and Y_2 are dependent. To make it easier, you can view the question as: "are Y_1 and Y_2 independent?"
[HW 4: Moments, variance, random sums] 4.21, 4.24, 5.3, 5.21, 5.26, 5.31, 5.33, 5.36, 5.38 in PnC textbook. Due 12:50 pm on 9/18.
- Note: We ran out of room to include a problem on Simpson's paradox, but if you want to see one, you can look at 4.17. Do not turn this in.
[HW 5: Inspection paradox, tails, Jensen, z-transform] 5.11, 5.20, 5.24, 5.30, 5.37, 6.2, 6.9, 6.11, 6.12, 6.14 in PnC textbook. Due 12:50 pm on 9/25.
[HW 6: Continuous R.V.s -- Single Variable] 7.2, 7.5, 7.6, 7.7, 7.8, 7.9, 7.11, 7.12, 8.14 in PnC textbook. Due 12:50 p.m. on 10/2.
- Problem 8.14 does not require any material from Chpt 8.
[HW 7: Multiple Continuous R.V.s] 8.4, 8.6, 8.8, 8.11, 8.13, 8.15, 8.17, 8.19. Due 12:50 p.m. on 10/9.