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Probability and Statistics course involves two parts: Probability Theory and Mathematical Statistics. The subject matter of Probability Theory is the mathematical analysis of random events, random variables, and random processes, based on Calculus I and II. The random events do not have deterministic regularity, but they possess statistical regularity, indicated by the stability of their relative frequencies (Kolmogorov’s Principle of the Modern Probability Theory). One fundamental result is the Central Limit Theorem. We view Statistics as encompassing the science of basing inferences on observed data and the entire problem of making decisions in the face of uncertainty. Statistics is a special theory of information, with procedures and methods for analyzing data that in some sense have a random character. We develop and interpret Statistics as “the technology of the scientific methods and their applications”.
Prerequisite: Calculus II
The main objective of probability theory is to develop stochastic calculus, including main rules of probability, discrete and continuous random variables, multivariate distributions, etc.
The main purpose of Mathematical Statistics is to make an inference about a population based on information contained in a random sample selected from that population, and to provide an associated measure of goodness for the inference. Another purpose is hypothesis testing for mean and variance.
Every Chapter of Probability and Statistics contains examples, problems and exercises on how to apply the concepts and methods.
Main textbook: Mathematical Statistics with Applications, by D. Wackerly, W. Mendenhall, R. Scheaffer, 6th edition, 2002 printed by Duxbury.
Schaum’s Outline of Probability and Statistics, by Murray R. Spiegel, John Schiller, and R. Alu Srinivasan, 2nd ed., 2000 printed by McGraw-Hill Companies Inc.
Upon completion of this course, students should be able to:
Content of the Course
Participation: Participation extends beyond mere attendance. Active participation is meant as the effort and the interest that a student shows in the class, including homework. After each session students are expected to study all the relevant material, read all the associated exercises, identify the difficult points and pose their questions in the next session either directly to me or in the class. You may miss up to three classes without penalty – your first two absences count whether you have a good excuse or not. Each absence beyond the first three will cost you points off of your participation grade. The only exceptions to this rule are severe illness (doctor’s note required) and UNYT approved trips/activities. Appropriate documentation for absences beyond the first three is necessary the class day directly before or after the one you miss. You are expected to attend class and I do keep attendance records. In general: this class is intensive and interactive. Missing class could seriously affect your grade! Students who are absent more than 20% of the total hours of the semester (i.e. 9 hours) may be required to withdraw from the course.
Class conduct: Exams are closed books. Also, you use your own calculator and nothing else will be allowed. Mobile phones are strictly not tolerated in the class for any use (including computations). Cheating and plagiarism in any form will result immediately in the grade F.
Students are responsible for everything that is announced, presented or discussed in class. The way to avoid any misunderstanding associated with this course is to attend class. Please, be courteous during class; both to me and your colleagues. I find late arrivals distracting, which cause a decline in the quality of my lecture. Importantly, it is also disruptive to your colleagues. Please, refrain from talking during class; it is disruptive to your colleagues and the lecture. I expect the best behavior from all of you. This is what education is all about. Please, consider that the language of instruction is English, so all our conversation into the class must be in this language.
Exams: Two examinations will be taken, a midterm exam during week seven of the course and a final exam covering all course content during the final examination period. Exam format may combine a mixture of short answer, true/false, matching, sort answer, and reasoning problems covering all readings, lecture, hand-out and class discussion content.
Final Examination: Monday, February 8, 2016, Time: 9:00 -12:00.
Deadlines in submitting the homework are critical. Therefore, late assignments and absence from tests will not be tolerated. In the event of illness or emergency, contact your instructor IN ADVANCE to determine whether special arrangements are possible. The University’s rules on academic dishonesty (e.g. cheating, plagiarism, submitting false information) will be strictly enforced. Please familiarize yourself with the STUDENT HONOUR CODE, or ask me or your advisor for clarification.
Grading scale follows the official UNYT as below:
|Letter Grade||Percent (%)||Quality Points||Generally Accepted Meaning|
|B+||87-89||3.33||Good work, distinctly above average|
|D+||67-69||1.33||Work that is significantly below average|
|F||0-59||0.00||Work that does not meet minimum standards for passing the course|
Assignments are to be word-processed and converted into pdf files. Continuing and regular use of e-mail is expected.
STUDENTS: If you feel that you have encountered special learning difficulties or serious problems that interfere with your studies, please make an appointment with UNYT Counseling Center, Dr. E Cenko (firstname.lastname@example.org) and/or the Academic Support Center, Dr. A Canollari (email@example.com). They are trained to help students with learning difficulties and have offered to provide this service to our students, just as it is offered in all American universities; you can also discus with your academic advisor.
If you need help with course content, please refer to the Math Center. Please feel free to talk to me for additional information.
Prepared by Prof. Dr. Fejzi Kolaneci