Applied Probability
APPM 3570
Spring 2011 Syllabus

  1. Course Goals: This course will provide the student with an orderly development of the fundamental principles of probability as well as an introduction to some of its applications and a bit of its history. Specifically, we will cover the axioms of probability, counting formulas, independence and conditional probability, discrete and continuous random variables, expectations, laws of large numbers and the central limit theorem, moment generating functions and the multivariate Gaussian distribution. (Prerequisite: Calculus III)

  2. Instructor: Dr. Anne Dougherty
    Office hours (Spring 2011): TBA or by appointment
    Office: ECOT 220
    Phone: 303-492-4011
    e-mail: Anne.Dougherty@colorado.edu

  3. Text: A First Course in Probability, 8th edition , by Sheldon Ross.

  4. Grading: There will be two hourly exams each worth 100 points, 6 unannounced quizzes worth 10 points each, homework worth 100 points, and a 150-point cumulative final. Please note that there will be no make-up exams or quizzes. The lowest quiz score will be dropped. If you are sick for an exam, you must bring a note from your doctor verifying your illness. Your course grade will then be determined from your remaining course work. Approximate grade lines will be 
            A-  --- 90% and above
        B-  --- 80% and above
        C-  --- 70% and above
        D   --- 60% and above
    Any adjustments made to this scale will be in the students' favor.

  5. Exams and Quizzes: The two unit exams will be announced one week in advance. Quizzes will be unannounced. Final: Wednesday, May 4 from 1:30 to 4:00 pm. Location: TBA

  6. Homework: Homework will be due on an approximately weekly basis. Late homework will not be accepted.

  7. Blue books: Each student is required to purchase three 8½"×11" blue books and to give them to me by the second week of class. These will be used for the exams.

  8. Special Accommodations: Any student eligible for and needing academic adjustments or accommodations because of a disability, religious beliefs, or athletic conflict should speak with me no later than Jan 24.

  9. Academic Honesty: Students may discuss homework problems with each other. However, all work turned in must be your own. Violation of the CU Student Honor Code will result in a course grade of F. Dropping the course: Advice from your department advisor is recommended before dropping any course. After Feb 23, dropping the course is possible only with a petition approved by the Dean's office.

    Some Goal Problems: By the end of the semester, you should be able to do these problems---and many more!

    The Birthday Problem: In a room filled with 370 people you would be sure to find at least two people with birthdays on the same day. If there were only two people in the room, it would be very unlikely that their birthdays would be on the same day. How many people would there have to be in the room before you would feel that there was at least a 50-50 chance of finding at least two of them with birthdays on the same day?

    The Matching Problem: Three politicians throw their hats into the ring. From the three hats, they each select one hat at random. What is the probability that no politician selects his/her own hat? What is the answer if there are 100 politicians? What is the answer if there are 1,000?

    Games of Chance: What is the probability of winning in a game of craps?

    Urn Problems: How many ways can you distribute b balls in n urns if (i) the balls are indistinguishable and the urns are distinguishable, (ii) both the balls and the urns are distinguishable, and (iii) the balls are distinguishable and the urns are not?

    Reliability Problems: The lifetimes of computer chips produced by a semiconductor manufacturer have a certain distribution. What is the probability that a batch of 100 chips will contain no more than 20 that are defective, i.e. whose lifetime is shorter than acceptable?

    A man and a woman agree to meet at a certain location about 12:30 PM. If the man arrives at a random time between 12:15 and 12:45 and the woman arrives at a random time between 12:00 and 1:00, find the probability that the first to arrive waits no longer than 5 minutes.