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Syllabus (updated on Oct 22 to include room for final exam)
HW assignments (problem numbers followed by * will be graded):
HW 1 (due Wed 09/28): sec 1.7: 1,3,7,10*,16*,19,20*,26*,27,28* (copies of exercises from chapter 1 of text)
solutions
HW 2 (due Wed 10/05): sec 1.7: 32*,37,38*,41,45,47*,48,51*,53,55* solutions Erratum: In 32a, P(ABA)=(0.7)(0.3)(0.7) should be added, giving a total probability of 0.784
HW 3 (due Mon 10/10): sec 2.7: 6,12,14*,16*,17*,22,25*,28,30* solutions
HW 4 (due Mon 10/17): sec 2.7: 41,42*,47,48*,53,54,59*,62,65* (note: an ace is higher than a 9 in bridge),67*
solutions (Typo: answer to 59a should be C_{30,4} instead of C_{40,3}; the numerical result is correct)
(copies of exercises from chapter 2 of text)
HW5 (due Wed 10/26): sec 2.7:78, 80*,82*, sec 3.5: 1,2*,3,4*,7*.
solutions. Erratum: In 3.5#2, B should have been the event that the sum is AT LEAST 9 instead of exactly 9. This changes the correct answer to 7/11.
(copies of exercises from chapter 3 of text).
HW6 (due Wed 11/02): sec 3.5: 21* (you can use, without proving, the table in Example 3.15 in the text showing the probabilities for the sum of 3 dice),25,34*,35,44*,46,47*,55*,56. solutions
HW7 (due Wed 11/09): sec 3.5: 62*,65, sec 5.6: 1,3*,8*,10*(but not part d),15,17* solutions
Erratum: For problem 10c, I accidentally used the bounds of problem 11c. So you should replace 1/9 by 1/3, and 1/4 by 2/3.
HW8 (due Wed 11/16): sec 5.6: 22*,25*,26,27,29*,30*,31* solutions Erratum: In problem 30, a term z should be added,yielding z-zlnz when z is in (0,1).(copies of exercises from chapter 5 of text)
HW9 (due Wed 11/23): sec 6.7: 1*,3,5*,9,10*,11,13*,14,16* solutions Erratum: In the last line of 13b, replace the power 2 for 0.1 by 1, and replace + by times (numerical answer is ok).
(copies of exercises from chapter 6 of text)
HW10 (due Fr 12/2): sec. 6.7: 17,19*,20*,21*,24*,27* solutions.
Announcements:
- Calendar for fall 2016.
- Link to some, but not all, errata in our text .
- Office hours on Mon Oct 3rd and Wed Oct 5th will run 10-10:50am instead of 10-11:15am because I have to sub a class for a colleague at 11am. Of course, you can also make an appointment for another time.
- There will not be an office hour on Wed Oct 19. Also, you will have a sub teacher for the lecture that day.
- The midterm on Mon Oct 24 will cover Chapters 1 (Basic Concepts) and 2 (Combinatorial Probability). Only problems will be on this midterm (no proofs of theorems; although you should understand the theorems we discussed in class and be able to apply them to solve problems). The problems will be similar to those we worked on in class, or which were part of the homework. I expect there to be between 5 and 10 problems on the midterm.
- Here are my own, handwritten lecture notes for chapter 1 and chapter 2. These are rough notes that you should only use to give you an idea what was covered in the various lectures. Often they omit things we discussed in more detail in class, e.g. the solutions to many exercises.
They may also contain typos and mistakes. Please keep these remarks in mind when you use these notes.
- I've been asked several questions about the midterm. Here is some information: The midterm will be closed book. You are not allowed to bring a calculator/phone/electronic device, or a formula sheet. Just bring pen(cil) and paper.
There will be between 5 and 10 problems. Some of these may be multiple choice questions, although I have not decided that yet. In any case, partial credit will be awarded to the open questions. I will not ask you to prove anything, so there is no need to study the proofs of the theorems we discussed in class. However, you will be expected to apply various theorems to particular problems. And yes, you do need to know/memorize the distribution function, expected value and variance of the handful random variables we've encountered so far (geometric,binomial and multinomial, Poisson).
- The final exam will be on Thursday December 8 from 2:00-3:50 in WNGR 287, our usual classcroom.
- Check out this international contest called the
Mathematical Competitive Game 2016-2017 inspired by Jules Verne's novel from the Earth to the Moon. The competition runs from Nov 1st, 2016 to April 30th, 2017. You can participate individually or as a group. Winners get to pick up their prize in Paris, France in May of 2017.
- Check out a new option in Mathematical Biology for math majors that was recently approved. Contact me in case you would like more information about it.
- For the final exam you can bring 1 formula sheet (1 side only) with 25 ``formulas". These could be definitions, or statement of theorems, or
specific formulas etc. But you are not allowed to write the answers to examples or problems on this sheet.
I will be checking each individual sheet during the final exam.
- Here are the lecture notes for chapter 3 and chapter 5. Same comments apply to those made for chapters 1 and 2 above.
- Here are the lecture notes for chapter 6. Same comments apply to those made for chapters 1,2,3 and 5 above.
- The grader mentioned that in HW 9, problem 16, many students concluded that X and Y are independent because their covariance is zero. This is not correct. As shown in class, independence of X and Y implies their covariance is zero. But the converse is not necessarily true.
The solution key shows why in this example, X and Y are not independent.
- There will be an additional office hour on Monday Dec 5 from 10:30 to 12:30.
- Here is the final exam, and here are the solutions.