01:640:477:H1   Mathematical Theory of Probability  

Course Schedule:    July 11~Aug 17, MTWTh   8:00-9:50 am   SEC-205, Busch Campus
Office Hour:            MTh  10:00-11:00 am (or by appointment)   Hill -622, Busch Campus
Course webpage:    math.rutgers.edu/~fantayu/477.html
Textbook:                Sheldon Ross, A First Course in Probability, 8th edition, ISBN # 978-0-13-603313-4, Prentice-Hall.

Required work:
 ° Reading:     Please read the sections covered in class after each lecture. Detailed numbers of sections will be listed with homework daily on Sakai and the course webpage.
 ° Homework: There will be five weekly homework assignments, due on each Monday (except the last one,  no homework due on 8/15). The homework will be collected at the start of each class. Late Homework will NOT be accepted.
 ° Quizzes:      There will be a 15-min quiz at the end of each Thursday lecture. If you pay attention in class and do all the homework, the quizzes will a snap.
 ° Exams:       There will be one midterm exam and one final exam. The date of midterm will be chosen between 07/28 (Thur) and 08/01 (Mon)--to be discussed in class. Final exam will occur on the last day of the course, i.e. 08/17, at 8:00~11:00 am in our regular lecture room SEC 205.
 NOTE: the final will be 3 hours long, around one hour longer than our regular classes. If you think you "might" have a time conflict on the final, make sure that you mention it to me as soon as possible.
updates: The date of midterm was discussed in class today and was agreed to be Monday, 08/01.

About midterm:
Schedule: Mon, 08/01, 8:00~9:50 am, SEC 205
Materials covered: Ch1~Ch4 (1.1~1.6, 2.1~2.5, 3.1~3.5, 4.1~4.9).
Formula sheet: will be provided with exam, containing inclusion-exclusion principle (the summation-subtraction formula), the law of total probability, multiplication rule of conditional probability, Bayes's formula, Poisson distribution.
Comment: There will be 10~12 problems, mostly based on quizzes and HW problems. Please go through your quizzes and HW thoroughly. In 07/28 (Thurs) class, I will have some review, and if time permits a couple of "challenging" problems can be discussed. If you have specific preferrence on problems to talk about, please let me know before the end of 07/27 (Wed).
Technical Suggestion: To solve any problem, unless notations are already given by the problem, please first write down your own definition of events, sample spaces, and/or random variables. This is good not only to make the procedure clear, but also in order not to confuse YOURSELF!
Other little things: "mutually exclusive" and "independent" are NOT the same!!! Indeed, if two events are mutually exclusive, then they are generally DEPENDENT on each other, because restrictions are put onto the outcomes of E and F, say, "F cannot take the outcomes of E" and vice versa. To see this more clearly, suppose events E and F are mutually exclusive, then EF=empty set, and P(EF)=0, but in general P(E)!=0 and P(F)!=0, and thus P(EF)!=P(E)*P(F)!
solution to midterm is posted online.

About final:
Schedule: Wed, 08/17, 8:00~11:00 am, SEC 205
Materials covered: Ch1~Ch8 (1.1~1.6, 2.1~2.5, 3.1~3.5, 4.1~4.9, 5.1~5.7, 6.1~6.5, 7.1~7.5, 7.7, 8.1~8.3).
Formula sheet: will be provided with exam, preview to be added later.
Comment: There will be 12~15 problems. Please go through your quizzes and HW thoroughly. You may also want to try some review problems (from Prof. Speer), a solution to most problems are posted. In 08/16 (Tue) class, I will have some review, and if time permits a couple of "challenging" problems can be discussed.

Solution to selected homework problems:
Ch4: 14 theoretical 2, 6
homework 4

Grading information:
Final exam:         200
Midterm exam:   100
Homework:          50
Quizzes:               50
Total:                 400

Calculators:      NO calculators needed.

 
Diary and Homework
°Preview of 07/11: sections 1.1~1.6.
°07/11 lecture
 sections 1.1~1.6 covered, please read the corresponding sections.
 homework 1 (part 1, due on Mon 07/18): Ch1(starting on page16): 6,7,16,26; theoretical (starting on page 18) problem 8 (you can either prove it "mathematically" or give a combinatorial explanation).
°preview of 07/12: 2.1~2.4. You may want to recall what you know about Venn diagram before, or go to the wiki page of Venn Diagram for a reference. I will also go through the introduction of it roughly in tomorrow's class.  
°07/12 lecture
 sections 2.1~2.4 covered, please read the corresponding sections.
 homework 1 (part 2, due on Mon 07/18): Ch2 (starting on page 50): 8, 10, 21; theoretical (starting on page 54) problem 7, 11.
°preview of 07/13: 2.5.
°07/13 lecture
 section 2.5 covered, please read the corresponding section.
 homework 1 (part 3, due on Mon 07/18): Ch2 (starting on page 50): 13,24,36,53,55; no theoretical problems.
 the quiz tomorrow will be based upon Ch1 (1.1~1.6) and Ch2 (2.1~2.5).
°preview of 07/14: 3.1~3.3.
°07/14 lecture
 sections 3.1~3.2 covered, section 3.3 started, please read the corresponding sections.
 homework 1 (part 4, due on Mon 07/18): Ch3 (starting on page 102): 4 (do for i=7,11), 16, 17, 19; theoretical (starting on page 110) problem 2.
 Make sure to get all the four parts of HW 1 ready by the beginning of Monday's class. Homework will be collected at the beginning of the lecture.
 solution to quiz 1 is posted online.
°preview of 07/18: 3.3~3.4.
°07/18 lecture
 sections 3.3~3.4 covered, please read the corresponding sections.
 homework 2 (part 1, due on Mon 07/25): Ch3 (starting on page 102): 18, 42, 47, 66; theoretical (starting on page 110) problem 6.
°preview of 07/19: More examples of section 3.4 will be added (which may help you solve HW problem 66), 3.5, 4.1.
°07/19 lecture
 sections 3.4~4.1 covered, please read the corresponding sections.
 homework 2 (part 2, due on Mon 07/25): Ch3 (starting on page 102): 73, 77, 83; theoretical (starting on page 110) problem 8, 11.
°preview of 07/20: finishing 4.1, 4,2~4,5, 4.9.
°07/20 lecture
 sections 4.1~4.5, 4.9 covered, please read the corresponding sections.
 homework 2 (part 3, due on Mon 07/25): Ch4 (starting on page 172): 14, 17, 25; theoretical (starting on page 179) problem 2, 6.
 the quiz tomorrow will be based upon Ch3 (3.1~3.5), 4.1~4.4, and 4.9.
°preview of 07/21: finishing 4.5, 4.6~4.7.
°07/21 lecture
 sections 4.5~4.7 covered, please read the corresponding sections.
 homework 2 (part 4, due on Mon 07/25): Ch4 (starting on page 172): 33, 38, 42, 58; theoretical (starting on page 179) problem 10.
 Make sure to get all the four parts of HW 2 ready by the beginning of Monday's class. Homework will be collected at the beginning of the lecture.
 solution to quiz 2 is posted online.
°preview of 07/25: finishing 4.7, 4.8. Moreover, since we will soon begin to work with integrations, please give yourself some review on differentiation and integration, esp. multivariable integration.
°07/25 lecture
 sections 4.7~4.8 covered, please read the corresponding sections.
 homework 3 (part 1, due on Tue 08/02): Ch4 (starting on page 172): 50, 59, 75, 78; theoretical (starting on page 179) problem 19.
°preview of 07/26: finishing 4.8, 5.1~5.2.
°Midterm on the coming Monday will be based upon Ch1~Ch4 (1.1~1.6, 2.1~2.5, 3.1~3.5, 4.1~4.9). Going through all quiz problems and homework problems will help you prepare for the test. I will give some review on Thursday, and if time permits, a couple of "problematic problems" from quizzes and homework will be discussed. If you prefer some problems to be mentioned in Thursday class, please send me an email before the end of Wednesday, I will try to cover the most "popular" choices. (There will still be a quiz on Thursday.)
°07/26 lecture
 sections 4.8, 5.1~5.2 covered, please read the corresponding sections.
 homework 3 (part 2, due on Tue 08/02): Ch5 (starting on page 224): 3, 4, 7, 8; theoretical (starting on page 227) problem 1.
°preview of 07/27: finishing 5.2, 5.3~5.5.
°07/27 lecture
 sections 5.2~5.4 covered, please read the corresponding sections.
 homework 3 (part 3, due on Tue 08/02): Ch5 (starting on page 224): 10, 11, 12, 15; theoretical (starting on page 227) problem 9.
 The quiz tomorrow will be based upon 4.5~4.8, 5.1~5.3.
°preview of 07/28: finishing 5.4, 5.5~5.6.+ review for midterm.
°07/28 lecture
 sections 5.4~5.6 covered, please read the corresponding sections.
 homework 3 (part 4, due on Tue 08/02): Ch5 (starting on page 224): 17, 18, 19; theoretical (starting on page 227) problem 2, 15.
 The due date of HW3 is changed to 08/02, considering the midterm. However, HW4 and HW5 later will still be due on Mondays.
 solution to quiz 3 is posted online.  
 Comments on today's class: Because of the time limit today, there are a couple of things I didn't manage to talk about in class today. Read the comment.
 The solution to a couple of homework problems are also posted: Ch4: 14 theoretical 2, 6
°preview of 08/01: midterm.
°08/01 midterm
 Solution key will be posted later. I will try to finish grading by Wednesday and hand out the exam on Thursday; but if not completed  in time, please aim at the coming Monday.
 Please be aware that HW 3 is due tomorrow, and will be collected at the beginning of the lecture.
°preview of 08/02: 5.7~6.1.
°08/02 lecture
 sections 5.7~6.1 covered, please read the corresponding sections.
 homework 4 (part 1, due on Mon 08/08): Ch5 (starting on page 224): 37, 38; theoretical (starting on page 227) problem 30; Ch6 (starting on page 287) 2,4.
°preview of 08/03: finishing 6.1, 6.4~6.5.
°08/03 lecture
 sections 6.1, 6.4 covered, please read the corresponding sections.
 homework 4 (part 2, due on Mon 08/08): Ch6 (starting on page 287): 6,8,10,38; theoretical (starting on page 291) problem 18.
 The quiz tomorrow will be based upon 5.4~5.7, 6.1, 6.4.
°preview of 08/04: 6.5, 6.2.
°08/04 lecture
 sections 6.5, 6.2 covered, please read the corresponding sections.
 homework 4 (part 3, due on Mon 08/08): Ch6 (starting on page 287): 17, 35, 40, 42; theoretical (starting on page 291) problem 20.
 Make sure to get all the three parts of HW 4 ready by the beginning of Monday's class. Homework will be collected at the beginning of the lecture.
 solution to quiz 4 is posted now.
°preview of 08/08: finishing 6.2, 6.3.
°08/08 lecture
 section 6.2 covered and 6.3 started, please read the corresponding sections.
 homework 5 (part 1, due on Wed 08/17): Ch6 (starting on page 287): 13, 18, 20, 21; theoretical (starting on page 291) problem 5.
°preview of 08/09: finishing 6.3, 7.1~7.2.
°08/09 lecture
 sections 6.3, 7.1~7.2 covered, please read the corresponding sections.
 homework 5 (part 2, due on Wed 08/17): Ch6 (starting on page 287): 22, 26, 46; Ch7 (starting on page 373) 4,6.
°preview of 08/10: finishing 7.2, 7.3~7.4.
°08/10 lecture
 sections 7.2~7.4 covered, please read the corresponding sections.
 homework 5 (part 3, due on Wed 08/17): Ch7 (starting on page 373): 9,15, 22, 38; theoretical (starting on page 380) problem 11.
 The quiz tomorrow will be based upon 6.2~6.3, 6.5, 7.1~7.3.
°preview of 08/11: finishing 7.4, 7.5, 7.7.
°08/11 lecture
 sections 7.4~7.5, 7.7 covered, please read the corresponding sections.
 homework 5 (part 4, due on Wed 08/17): Ch7 (starting on page 373): 40, 45, 48, 50; theoretical (starting on page 380) problem 25.
 solution to quiz 5 is posted now.
°preview of 08/15: finishing 7.7, 8.1~8.3.
°08/15 lecture
 sections 7.7, 8.1~8.3 covered, please read the corresponding sections.
 homework 6 (this part will not be collected): Ch7 (starting on page 373): 76; Ch8 (starting on page 412): 1,2,3,4. Make sure you understand the statements of the theorems and propositions we've talked about in class today, since they won't be on the formula sheet.
 solution keys to HW4 and most of review problems are posted.
°preview of 08/16: review. Bring all your questions!
°08/16 review
 review for all materials after midterm done, and questions in HW5 answered. If you still have questions on quizzes, HWs and the midterm, please don't hesitate to ask. Concerning the review sheet, if you are out of time working on specific problems, simply go through the solution and see how to get started, as this is really a good chance to digest what we've learned in the whole semester.
There will be a review session tonight 7~8pm in Hill 423. (I said Hill 622 earlier today in class, but it seems better for us to use a regular classroom, sorry for the late notice.) A preview of formula sheet is posted now.
BTW, the survey for this course is going to end by 11:59pm today. If you haven't done it and still want to finish it, please log into Sakai with your NETID and click on "all surveys", then go ahead. :-)
°preview of 08/17: final, for 3 hours, no calculators needed.
°08/17 final exam
The grades will be posted by the end of Friday. You should be able to check online for your score. I've been told that instructors are not allowed to reveal grades to students through email, so please check directly through the online system. Enjoy the rest of the summer!