Vaughn Climenhaga

Associate Professor
Department of Mathematics
University of Houston


Math 3338

Probability
Fall 2015



Sample formula sheet
(this or something very close to it will be provided on the final exam)

Comments and suggestions
for preparing for the final exam



Instructor:
Vaughn Climenhaga
  • Office: 665 PGH
  • Office hours:  Monday 9-9:50am, Wednesday 1:30-2:30pm
  • Email: climenha [at] math.uh.edu

Course details:
  • Lectures:  MWF, 12-1pm, CBB 104
  • Textbook:  Introduction to Probability and its Applications, third edition, by Richard L. Scheaffer and Linda J. Young.
    Note that there may be different textbooks used for Math 3338 depending on which section you are enrolled in.  Be sure you have the appropriate textbook for this section.
  • Course syllabus

Important dates:

  • Mon, Aug 24: Lectures begin
  • Tue, Sep 1: Last day to add a class
  • Mon, Sep 7: No class (Labor Day)
  • Wed, Sep 9: Last day to drop or withdraw without receiving a grade
  • Fri, Sep 25: Test #1 (in class)
  • Wed, Oct 21: Test #2 (in class)
  • Fri, Oct 23:  No class
  • Fri, Oct 30: Last day to drop or withdraw with a "W"
  • Wed, Nov 25 and Fri, Nov 27: No class (Thanksgiving)
  • Fri, Dec 4: Last day of class
  • Fri, Dec 11: Final exam (11am-2pm, regular classroom)

The goal of this course is to provide a basic background in probability theory that will enable students to pursue further studies in the many areas that rely on the tools of probability, and to be generally conversant in the role that probability plays in the world around us.

Topics to be covered include sample spaces, events, and probabilities; random variables and distributions, expectations, variances and covariances; basic discrete and continuous distributions; and the central limit theorem.

In addition to the office hours listed above, you are encouraged to make use of the tutoring resources available to you at CASA.

Homework assignments

HW 1 (due 8/28): exercises 2.6, 2.10, 2.14

HW 2 (due 9/4):
exercises 2.18, 2.28, 2.44, 2.50

HW 3 (due 9/11):
exercises 2.52, 2.56, 2.62, 2.66

HW 4 (due 9/18):
exercises 2.72, 2.86, 2.88, 2.92, 3.6, 3.8
For 2.72, find the strategy that maximizes the probability that neither outdated passport is detected.  For 2.86, remember that the face cards are J,Q,K in each suit.
Review questions for Test #1 (not collected or graded): 2.43, 2.45, 2.55, 2.60, 2.77, 2.83, 2.84, 2.91, 3.16, 3.20, 3.22, 3.28, 3.31, 3.36, 3.40, 3.44, 3.54

HW 5 (due 10/2): exercises 3.44, 3.52, 3.58, 3.62

HW 6 (due 10/9): exercises 4.2, 4.8, 4.10, 4.14, 4.22

HW 7 (due 10/16): exercises 4.30, 4.32, 4.34, 4.44, 4.54, 4.56

Review questions for Test #2 (not collected or graded): 3.64, 3.68, 3.73, 4.4, 4.18, 4.33, 4.45, 4.52, 4.157, 4.160

HW 8 (due 10/30): exercises 4.76, 4.78, 4.94, 4.98, 4.114

HW 9 (due 11/6): exercises 4.127, 4.131, 4.134, 4.140, 5.4

For 4.134, find a closed form expression for the probability generating function (that does not involve a summation formula).

HW 10 (due 11/13): exercises 5.18, 5.24, 5.38, 5.50, 5.60, 5.68

HW 11 (due 11/20): exercises 5.80, 5.84, 5.96, 5.130, 5.136

For the exercises involving the normal distribution, use Table 4 in the Appendix (p. 448).  The entries of the table give the area underneath the Gaussian curve between 0 and z, for different values of z.  The left-most column (labeling the rows) gives z up to the nearest tenth, and then the top row (labeling the columns) gives z up to the nearest hundredth.  So for example, to find the area underneath the curve between 0 and z=0.82, we would look in the row labeled "0.8" and the column labeled ".02", to read off the value .2939.  You can also find the numerical values using software of your choice (Matlab, Mathematica, etc.), or an online tool such as Wolfram Alpha.

HW 12 (due 12/4): exercises 6.6, 6.10, 6.26, 6.32, 6.72

Final exam review assignment (not collected or graded): note that numerical answers to most odd-numbered exercises are in the back of the book.

    Chapter 2: exercises 41, 47, 57, 67, 87
    Chapter 3: exercises 19, 29, 35, 41, 51, 72
    Chapter 4: exercises 55, 79, 95, 97, 128, 132, 139, 169
    Chapter 5: exercises 25, 37, 45, 52, 69, 99, 135, 140, 141, 161
    Chapter 6: exercises 14, 23, 35, 37, 87

If you want more practice after completing those, the following are recommended.

Exercises 2.11, 2.23, 2.39, 2.51, 3.5, 3.9, 3.21, 3.33, 4.27, 4.42, 4.61, 4.83, 4.111, 4.133, 5.11, 5.81, 5.104, 5.168, 6.27, 6.40, 6.85