Probability, MATH 511 and STAT 511

Instructor: George Androulakis, giorgis@math.sc.edu, (803)777-7539
Lectures: MWF 10:50-11:40 in LeConte 422
Instructor’s Off. H: MWF 9:45-10:45, or by appointment in LeConte 402.

Learning outcomes: The students will be expected to learn the following learning outcomes.

• Know the laws of probability, how to use Ven diagrams, and to represent unions, intersections.

• Know what does it mean for some events to be independent.

• Know the law of total probability and the Bayes rule.

• Know the multiplication principle and how to use it.

• Know the formulas for counting the numbers of Ordered/Unordered samplings with/without replacement.

• Know the meaning and Probability Mass Function (PMF) for the following discrete r.v.’s : Bernoulli($p$), Binomial($n$,$p$), Geometric($p$), Pascal($m,p$), Hypergeometric($b,r,k$), Poisson($\lambda$).

• Know the meaning andthe Probability Density Function (PDF) for the following continuous r.v.’s: Uniform$(a,b)$, Exponential$\left(\lambda \right)$, Normal$(\mu ,{\sigma }^2)$.

• Know the definitions of Cumulative Distribution Function (CDF), Probability Mass Function (PMF), Probability Density Function (PDF) and know how to use them in order to compute probabilities.

• Know how to compute the Expectation, Variance, and Standard Deviation of a r.v.

• Know how to compute the CDF of functions of r.v.’s.

• Know how to compute the marginals of joint distributions, and how to use the joint PMF or joint PDF in order to compute probabilities.

• Know the formula of the Moment Generation Function MGF.

• Know that the Expectation is linear. Know that the variance of the sum of independent r.v.’s is equal to the sum of the variances. Know that for computing the variance of a linear combination of independent r.v.’s the coefficients get squared. Know that a linear combination of independent Normal r.v.’s is also Normal, and know to compute its mean and variance.

• Know the Chebychev’s inequality and how to use it.

• Know the Central Limit Theorem CLT and how to use it.

Text: A first Course in Probability, by Sheldon Ross, 10th Edition.

Prerequisites: Completion of Math 241 with a grade of C or higher.

Grading: Your final grade will be computed by the formula:

$\mathbf{\text{Numerical grade}}={\displaystyle \frac{1}{5}}(\text{Quiz Grade}$ $+\text{Homework Grade}+\text{First Midterm}$

$+\text{Second Midterm}+\text{Final Exam}).$

Each of the Quizzes, Homeworks, Midterm Exams, and Final Exam will be graded out of 100 points, so your numerical grade will also be out of 100 points. At the end of the class, your grade will be converted to a letter grade according to the scale: [0, 60) $\Rightarrow$ F, [60, 65) $\Rightarrow$ D, [65, 70) $\Rightarrow$ D+, [70, 75) $\Rightarrow$ C, [75, 80) $\Rightarrow$ C+, [80, 85) $\Rightarrow$ B, [85, 90) $\Rightarrow$ B+, [90,100] $\Rightarrow$ A.

Homework: It will be assigned regularly and graded via the MyMathLab. To access the MyMathLab, click here. See the document entitled “MyMathLab_Student_Registration_Instructions.pdf”that you will find inside Blackboard in order to register in MyMathLab. The lowest homework grade will be dropped. The homework deadlines will be strictly observed, and they will not be changed, so make sure that you start working on your homework as soon as they are assigned.

How to work on the Homework: Always when I learn a new concept I have some misconceptions and wrong understandings. These are responsible for my first few of mistakes when I try to solve problems related to these new concepts. That is why MyMathLab will give you three opportunities for each problem. If you use computer aid or tutors to solve the homework, then you avoid making these wrong attempts at the homework (for which your first two wrong solutions will be forgiven anyways!). Thus you risk of making the first wrong attempts at the quizzes or the exams (for which a wrong solution penalizes you). Thus, I recommend that you work on the homework on your own in order to understand the materials better and maximize your performance in the quizzes and exams.

Quizzes: Every Friday except the first Friday of the semester, the last two Fridays of the semester, the Friday of Spring Break, and the Fridays that will be used for midterms we will have a quiz. The quizzes will be based on the homework assignments. Calculators, cellphones, computers, books or notes will not be allowed during quizzes. For each excused missed quiz you can take a make-up quiz. Friday April 17th is the designated make-up quiz/exam day, (for all students who have excused quizzes/exams). The lowest quiz grade will be dropped. Unexcused missed quizzes will count for zeros. Therefore, the lowest quiz grade will be a zero if there is an unexcused missed quiz. Your Quiz Grade will be the average of all your quiz grades not counting the lowest quiz grade. If you must miss a quiz day, then you may try to excuse your missed quiz by filling out the form which is provided by the Office of Student Advocacy. If their office accepts your excuse, then they will send me (and they will carbon copy you) an official excuse letter.

Condition on Quizzes: We will only be able to have quizzes if we will be assigned a grader. I hope that we will be assigned a grader but always there is some uncertainty about it. If we will not be assigned a grader, then we will not have quizzes, and the factor $\frac{1}{5}$ in the formula that gives the numerical grade will change to $\frac{1}{4}$.

Exams: There will be two Midterm Exams whose tentative dates are listed below. The exams will be based on the homeworks. Calculators, cellphones, computers, books or notes will not be allowed during exams. If you must miss an exam, then you may try to excuse your missed exam by filling out the form which is provided by the Office of Student Advocacy. If their office accepts your excuse, then they will send me (and they will carbon copy you) an official excuse letter. In that case you can take a make-up exam on the make-up quiz/exam day (Friday April 17th).

The second Midterm Exam will cover the new materials since the first Midterm Exam. After the second Midterm Exam we will learn some more materials as well as we will review. The Final Exam will be comprehensive.

Important dates:

• Monday January 12: first day of classes.

• Monday January 19: Dr. Martin Luther King, Jr. Service Day, (no classes).

• Friday February 20: tentative date for the first midterm exam.

• March 8-15: Spring break (no classes).

• Monday March 30: last day to drop a course or withdraw without a grade of ”WF” being recorded.

• Friday April 10: tentative date for the second midterm exam.

• Friday April 17: the designated make-up quiz/exam day for all students who have excused quizzes/exams.

• Monday April 27: last day of classes.

• Monday May 4 at 9 a.m.: the final exam.

Academic honesty: Cheating and plagiarism will not be tolerated in this course. Violations of this policy will be dealt with a matter consistent with University regulations.

Cell phones, computers and newspapers: Turn off cell phones during classes. You are not permitted to use computers or read a newspaper inside the classroom, because this distracts the rest of the students and me.