HOMEWORKS

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] 1.2, 1.3, 1.4, 1.6, 1.7 in PnC textbook, plus 1.12 and 1.13 in this pdf file. Please read the instructions in the pdf file. Due 12:50 pm on 1/19.
[HW 2: Events and R.V.s] 2.1, 2.7, 2.8, 2.10, 2.11, 2.17, 2.22, 2.28, 3.8 in PnC textbook. Due 12:50 pm on 1/26. 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: R.V.s and expectation] 3.5, 3.12, 4.4, 4.10, 4.12, 4.14, 4.16, 4.18, 4.26 in PnC textbook. Due 12:50 pm on 2/2.
- Problem 3.5: The reference to Definition 3.3 is a typo. We should refer to Definition 3.5.
- Problem 3.12: Each sub-question asks if Y_1 and Y_2 are dependent. To make it easier, you can take the question as "are Y_1 and Y_2 independent?"
[HW 4: Simpson's, moments, random sums] 4.17, 5.2, 5.24, 5.29, 5.30, 5.31, 5.36, 5.37, 5.38 in PnC textbook. Due 12:50 pm on 2/9.
[HW 5: Inspection paradox, z-transform] 4.21, 5.20, 6.2, 6.8, 6.9, 6.11, 6.12, 6.14, 6.15 in PnC textbook; Extra Credit: 6.16 in PnC textbook. Due 12:50 pm on 2/16.
[HW 6: Continuous R.V.s] 7.2, 7.5, 7.7, 7.8, 7.9, 7.11, 7.12, 8.14 in PnC textbook, plus 8.31 in this pdf file. Due 12:50 pm on 2/23.
[HW 7: Multiple Continuous R.V.s] 8.4, 8.8, 8.11, 8.13, 8.15, 8.17 in PnC textbook. Due 12:50 pm on 2/28 (Wed).
[HW 8: Multiple Continuous R.V.s, Normal distribution, heavy-tailed distribution] 8.12, 8.19, 8.21, 9.3, 9.5, 9.6, 9.7, 10.1, 10.2 in PnC textbook. You don't need to read Chapter 10 to do 10.1 and 10.2. Due 12:50 pm on 3/15.
[HW 9: Heavy-tailed distribution, Laplace transform] 10.3, 10.5, 10.8, 11.2, 11.5, 11.8, 11.9, 11.11, 11.12 in PnC textbook. Due 12:50 pm on 3/22.
- Hint for 11.11: you may want to look at Exercise 11.10 first.
[HW 10: Poisson processes] 12.5, 12.6, 12.7, 12.10, 12.11, 12.13, 12.14, 12.15, 12.16 in PnC textbook. Due 12:50 pm on 3/29.
[HW 11: Generating r.v.s and simulations] 13.1, 13.2, 13.3, 13.4, 13.5, 13.6, 14.1, 14.2, 14.3 in PnC textbook. Due 12:50 pm on 4/6 (Saturday).
Note: We're giving you an extra day, but encourage you to do the problems -- even if you don't write them up -- before the midterm).
Note: There will be no homework due on Friday April 12 (Carnival).
Some notes about the exercises in Chapter 14:
- The problems in chapter 14 require writing some code. Please take a snapshot of your code and submit that with the exercise.
- Use any programming language you want, but make sure that your code involves event-driven simulation, as discussed in chapter 14. It should be clear in your code how you're generating the needed random variables (using what we learned in chapter 13) and how you're computing the performance metrics.
- When obtaining performance metrics from your simulation, we recommend using a very large number of arrivals (at least 10^6, but you may need more).
- Because not all of you are comfortable writing code, we are fine with your doing the chapter 14 problems in pairs. If you choose to do this as part of a pair, each of you should submit the same code and should note your partner's name on the problem. It is your job to find a partner, so please start looking early.
[HW 12: Covariance, sample mean and variance, MLE] 5.13, 5.14, 5.17, 15.2, 15.4, 15.5, 15.6, 16.2, 16.3, 16.5 in PnC textbook. Due 12:50 pm on 4/19.
[HW 13: Bayesian estimation, confidence interval] 16.6, 16.7, 16.8, 17.3, 17.4, 17.5, 17.7, 17.8, 19.4 in PnC textbook. Due 12:50 pm on 4/26.