AMS311: Probability Theory, Spring 2004

FINAL EXAM SCHEDULE: Wed, May 19th, 8:30-10:30am,  Harriman 108
EARLY EXAM: Friday, May 14th, 5:00-7:00 pm, Physics P128  (Please prensent your registration to the acturial exam when you take the early exam)

The final exam will have two parts. Part I (Exam 3) covers the material after exam 2 and is mandatory. Part II (the second chance exam) covers the material before exam 2 and is optional. Scores from Part II will replace the lower score of the exam 1 and exam 2. Each part takes 1 hour.

YOU WILL GET BOTH EXAMS TOGETHER AND THEY WILL BE COLLECTED TOGETHER AT THE END OF TWO
HOURS. You do not have to let me know your decision before the exam.

The exam is close book, close notes and  the calculators are not allowed. However, you are entitled to bring in a letter size cheat sheet (8.5 inch by 11 inch), you can write on both sides and must have your name on it. Only one sheet is allowed regardless whether you are taking the second chance exam or not.

Practice Exam of Exam 3 (Part I of the final)
Solution
The solution of problem3 is wrong, the correct answer is below
a) p = P(X<300)=1-P(X>300)>1-E(X)/300 =0.2
b) p = P(X<300)=1-P(X>300)>1-P(|X-240|>60)>1-0.25=0.75
 

Extra Office Hours for the final
May 12, 3-6pm
May 18, 9am-12noon
 
 

Instructor:

Dr. Kenny Ye, Math Tower 1-117, 632-9344, kye@ams.sunysb.edu

Office hours: MW 1:00-2:30, or by appointment. If you would like to stop by and I am in my office and not busy at the moment, I could spend 5-10 minutes answering you questions.

Course Web Site:

http://www.ams.sunysb.edu/~kye/ams311.html

Teaching Assistant:

Jasmin Divers, Harriman 018, Room 6
Office hours: TuF 11:30-12:30
Email: jadivers@ams.sunysb.edu

Lecture

10:40-11:35, MW,  Harriman 108

Pre/Corequisites:

AMS 261, MAT 203 or 205. We will be using a fair amount of calculus, including some calculus of two variables (double integration).

Text:

A First Course in Probability, 6th Edition, by Sheldon Ross (Prentice Hall, ISBN 0-13-033851-6).  Textbook website

You may also find helpful The Probability Problem Solver, or the book The Probability Tutoring Book by Carol Ash; these books have a huge number of solved examples and problems.

Homeworks:

There will be 8 homework sets, equally weighted, and I will drop the lowest one score before computing your average. Homework will be due at the beginning of class on the due date.

Homework Policy:

No late homework will be accepted. (Since I drop the lowest score, missing a homework due to illness should not be a problem.) You may discuss homework problems with other students currently taking the course, with the TA, and with the instructor. But the work that you turn in should always be your ownwrite-up, and you should show that you personally understand everything that you write. Please make certain that your writing is neat and clear, and that you have expressed your reasoning, not just the final answer. Please staple!

Exams:

There will be three exams, equally weighted, with the first two given in class (Feb 25, Mar 31), and the third given during the first half of the final exam period ( Wednesday, May 19th, Period 1: 8:00am-10:30am). During the second half of the final exam period you have the option to do a ``Second Chance Exam'' which covers the material of the first two exams; I will use the higher of your two scores on that exam in computing your average.

Grades:

Your total average score will be 10% homework, plus 30% per exam. I will use your total average score to assign a letter grade; there is no pre-established scale or curve. (If there is a huge disparity among different exam averages, I may, at my discretion, curve the numbers before computing the weighted average above.)

Course Outline:

The following topics will be covered, with some variation depending on the availability of time:

$\bullet$ Probability -- definitions and basic concepts

$\bullet$ Conditional probability and independence

$\bullet$ Discrete random variables, special distributions

$\bullet$ Continuous random variables, special distributions

$\bullet$ Joint distributions -- several random variables; covariance

$\bullet$ Conditional distributions

$\bullet$ Sums of random variables; moment generating functions

$\bullet$ Laws of large numbers -- limit theorems

Cheating Policy:

This is very clear and very simple: Cheating, to any degree, will result in an automatic failure of the course, prosecution to the fullest extent of the law (e.g., dismissal), and a letter placed on permanent file with the University. There are no excuses for cheating; if you have extenuating circumstances, see me *before* you even contemplate cheating.

Disability Policy:

If you have a physical, psychological, medical or learning disability that may impact your course work, please contact Disability Support Services, ECC (Educational Communications Center) Building, room 128, (631) 632-6748. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential. Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and Disability Support Services. For procedures and information, go to the following web site: http://www.ehs.sunysb.edu/fire/disabilities.asp
 



Homework Assignments and Solutions, Other handouts

Homework 1, Solution
Homework 2 ,Solution
Homework 3 ,Solution(The solution of third problem is incorrect, errata)
Homework 4, Solution
Homework 5, Solution (the solution of 3(b) is wrong, use Poisson with lambda=9 instead)
Homework 6, Solution
Homework 7, Solution
Homework 8, Solution(A graph that explains 2b)
Homework 9, Solution
Lecture Handouts

Practice Exams
Practice Exam for the First Midterm, Solution
Practice Exam for the Second Midterm, Solution, Correction
There are numerous mistakes in the original solutions.
2(e) P(X>2.5)/P(X>0.1)=0.3/0.6

3(c) The CDF function should be F(y)= (y-40)^2/6400. The function in the solution is the PDF

5(a) wrong at the end. should be 1-P(X>3) = 1-e^(-3/5). Note that lambda=1/5 since E(X)=5.
 

Solution of Exam I
Solution of Exam II

Distirbution of Exam II grade
100         1
95-99    10
90-94    7
80-89    12
70-79    13
60-69    9
    -59    11


 
 

Links of Interest to the Course:

Ross textbook website
The Probability Problem Solver, a study guide with lots of solved problems.
Brief report on Monty Hall problem, by Afra Zomorodian
Probability Puzzles
Cut-the-Knot Probability Page
The Problem Bank, with several cute puzzles
Chance Web Page, real-life uses of probability and statistics (co-authored by my office-mate from Stanford, Bill Peterson)
MaxValue, Decision Analysis and Project Risk Management
Nick's Mathematical Puzzles, with several nice probability puzzles, including some classics!
Conditional Probability Discussion
 

For Your Amusement:

I know two distinct secret numbers: call them X and Y, and assume that X < Y, without loss of generality. You have no clue how I came up with them. They could be anything (positive, negative, rational, irrational, etc). They could come from any probability distribution (discrete or continuous). You have no idea. I flip a fair coin. If the coin shows Heads, I reveal to you the larger number, Y; if it shows Tails, I reveal to you the smaller number, X. You do not get to see the result of the coin flip. Your goal is to guess whether the coin was Heads or Tails, based only on your seeing the one number that I revealed to you. Obviously, if you just decide ``Heads'' is your guess, without taking into account the revealed number at all, then you are correct with probability 0.5. But your goal is to be able to be correct with probability {\em strictly greater} than 0.5. Devise a method to do this, and explain your solution.


You have two ropes. Each takes exactly 60 minutes to burn. They are made of different material so even though they take the same amount of time to burn, they burn at separate rates. In addition, each rope burns inconsistently. How do you measure out exactly 45 minutes? (You are to assume that, while the speed of the rope burning may vary with position x along the rope, the speed of burning to the right at x is the same as the speed of burning to the left at x.)


Two engineering students had thoroughly impressed their Professor in one of their core subjects, having achieved the highest marks throughout the semester's continuous assessments. Being one to give credit where due, the Prof made no secret of his two prize students, continually praising their achievements. The weekend before their final exam (which was to contribute fifty percent of their final grade,) these two geniuses felt they deserved a hard earned break and so went out of town to celebrate their 'pending' success. Having partied late all weekend (and then some,) the two students overslept Monday morning, missing their final exam! Never lacking in will power, they were determined not to fail, having come so far, so well. Upon rolling into town, they appealed to the Prof, and conveniently explained that they had a flat tire while out visiting and that it was not their fault for missing the exam. The Professor was very understanding and rescheduled their exam to the next day, much to the student's delight! They arrived at his office the next morning, where he sat them on each side of his desk facing opposite walls, while he worked on grading the other exams. They opened their examination books and were both pleased with the first easy 10-point question that came directly from a homework assignment. You could hear nothing but the quick writing of their pencils in the room, until they both flipped the page, almost at the same time, where the second question read thusly... "90 points: Which tire?"