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COURSE NAME: "Mathematical Statistics"
SEMESTER & YEAR: Fall 2019

INSTRUCTOR: Stefano Arnone
EMAIL: [email protected]
HOURS: TTH 4:30-5:45 PM
PREREQUISITES: Prerequisites: MA 198, MA 208, MA 209; Recommended: MA 299
OFFICE HOURS: TTh 2:15 to 3:00 pm and 6:00 to 6:30 pm by appointment

This is a calculus-based introduction to mathematical statistics. While the material covered is similar to that which might be found in an undergraduate course of statistics, the technical level is much more advanced, the quantity of material much larger, and the pace of delivery correspondingly faster.  The course covers basic probability, random variables (continuous and discrete), the central limit theorem and statistical inference, including parameter estimation and hypothesis testing. It also provides a basic introduction to stochastic processes.

The course covers basic probability theory as stemming from the axiomatic definition of probability; random variables (continuous and discrete); the central limit theorem and statistical inference, including parameter estimation. It also provides a basic introduction to stochastic processes.


Upon successful completion of the course, students will be able to apply the various techniques they learned in calculus to the field of Statistics. In particular, they will:

- understand  the concepts of probability distributions and distribution functions;

- understand random variables and their distributions;

- understand the moments, joint moments and moment generating functions of the random variables;

- be able to derive the distributions of functions of random variables;

- be able to state and apply the Central Limit Theorem;

- understand simple stochastic processes.

Book TitleAuthorPublisherISBN numberLibrary Call NumberComments
The Concepts and Practice of Mathematical FinanceMark JoshiCambridge University Press9780321500465 This is suggested material only.
Probability and Statistics, 4th editionMorris H. DeGroot and Mark J. SchervishAddison-Wesley Pearson9780321500465  

HomeworkHomework assignments will be graded: the average grade weighs 15 percent of the final grade. At the professor's discretion, late assignments might not be accepted.15/100
Attendance and class participationFull credit for attendance will be given to students with three or fewer unexcused absences. Four or more absences will result in a proportional reduction of the grade.15/100
Mid-term exam 30/100
Fianl exam (comprehensive) 40/100

AWork of this quality directly addresses the question or problem raised and provides a coherent argument displaying an extensive knowledge of relevant information or content. The student demonstrates complete, accurate, and critical knowledge of all the topics, and is able to solve problems autonomously.
BThis is highly competent level of performance and directly addresses the question or problem raised.There is a demonstration of some ability to critically evaluate theory and concepts and relate them to practice. The work does not suffer from any major errors or omissions and provides evidence that the student uses clear logic in his/her arguments.
CThis is an acceptable level of performance and provides answers that are clear but limited, reflecting the information offered in the lectures. Mathematical statements are properly written most of the time.
DThis level of performances demonstrates that the student lacks a coherent grasp of the material. Important information is omitted and irrelevant points included. Many mistakes are made in solving the problem raised. In effect, the student has barely done enough to persuade the instructor that s/he should not fail.
FThis work fails to show any knowledge or understanding of the subject-matter. Most of the material in the answer is irrelevant.


Full credit for attendance will be given to students with three or fewer unexcused absences. Four or more absences will result in a proportional reduction of the grade. Coming late to class or leaving early will be possible only with permission of the instructor.

Major exams (midterm or final) cannot be made up without the permission of the Dean’s Office. The Dean’s Office will grant such permission only when the absence was caused by a serious impediment, such as a documented illness, hospitalization or death in the immediate family (in which you must attend the funeral) or other situations of similar gravity. Absences due to other meaningful conflicts, such as job interviews, family celebrations, travel difficulties, student misunderstandings or personal convenience, will not be excused. Students who will be absent from a major exam must notify the Dean’s Office prior to that exam. Absences from class due to the observance of a religious holiday will normally be excused. Individual students who will have to miss class to observe a religious holiday should notify the instructor by the end of the Add/Drop period to make prior arrangements for making up any work that will be missed.
The Instructor reserves the right to choose days and times for make-up exams that best fit his schedule, after consulting the student(s) involved.

As stated in the university catalog, any student who commits an act of academic dishonesty will receive a failing grade on the work in which the dishonesty occurred. In addition, acts of academic dishonesty, irrespective of the weight of the assignment, may result in the student receiving a failing grade in the course. Instances of academic dishonesty will be reported to the Dean of Academic Affairs. A student who is reported twice for academic dishonesty is subject to summary dismissal from the University. In such a case, the Academic Council will then make a recommendation to the President, who will make the final decision.
John Cabot University does not discriminate on the basis of disability or handicap. Students with approved accommodations must inform their professors at the beginning of the term. Please see the website for the complete policy.


SessionSession FocusReading AssignmentOther AssignmentMeeting Place/Exam Dates
Week 1 and week 2Review of Probability TheoryDe Groot (DG), Chaps 1 and 2  
Week 3 to week 6Random Variables and their probability distributionsDG, Chap. 3, sects 3.1 to 3.5 and 3.7 to 3.9 DG, Chap. 5, sects 5.5 to 5.7 DG, Chap. 8, sects 8.2 and 8.4   
Week 7ExpectationDG, Chap. 4, sects 4.1 to 4.6 Week 7 or beginning of week 8: mid-term exam (Topics: probability theory and distributions of random variables)
Week 8The Central Limit theoremDG, Chap. 6 Week 7 or beginning of week 8: mid-term exam (Topics: probability theory and distributions of random variables)
Week 9Estimation DG, Chap. 7, sects 7.5 and 7.6   
Week 10 to week 13Stochastic processes and the Ito calculus Joshi (J), Chap. 5, pp. 89 to 104  
Week 14The Black-Scholes equationJ, Chap. 5, pp. 104 to 113 Final Exam COMPREHENSIVE. See University Schedule for date and time.