Course Syllabus

Office Hours: Tuesdays 10:00-11:00, Office 1st floor

Phone: +355 4 4512345


Catalog Description


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

Course Purpose:

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.


Required Readings:

Main textbook: Mathematical Statistics with Applications, by D. Wackerly, W. Mendenhall, R. Scheaffer, 6th edition, 2002 printed by Duxbury.


Additional textbooks:

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.

Course Objectives

Upon completion of this course, students should be able to:

  1. Calculate the probability of a random event.
  2. Use the main rules of probability, including conditional probability, independent random events, the law of total probability and Bayes Rule.
  3. Know and apply discrete random variables and distributions: pdf, mean, variance.
  4. Know and apply continuous random variables and distributions: pdf, mean, variance.
  5. Perform transformations of the probability function.
  6. Develop multivariate discrete or continuous distributions.
  7. Know and apply Binomial, Poisson and Normal Distribution.
  8. Apply χ2 , t, and F distribution in various fields of human activity or nature.
  9. Develop confidence interval for the mean of a population (large sample case versus small sample case).
  10. Use the maximum likelihood estimation method


Content of the Course


  1. Descriptive Statistics: Measures of location, dispersion, asymmetry, kurtosis.


  1. Probability: Basic definitions and concepts, addition and multiplication rules, independent and mutually exclusive events, tree diagrams. Total probability formula Bayes’s formula.


  1. Counting Methods. Discrete random variables and distributions: probability mass function and cumulative distribution function, mean and variance.


  1. Continuous random variables and distributions: probability density function and cumulative distribution function, mean and variance, mode, median.


  1. The moment generating function.


  1. Transformations of the probability function.


  1. Multivariate discrete distributions: conditional, joint and marginal probability functions. Conditional expectations.


  1. Multivariate continuous distributions: conditional, joint and marginal probability density functions. Conditional expectations.


  1. The Bernoulli, Binomial and Poisson Distributions. Approximation of Binomial distribution to Poisson distribution.


  1. The Normal Distribution Model and the Standard Normal Distribution Model. Approximation of Poisson to Normal.


  1. Estimation Theory: Estimators, Estimates. The Central Limit Theorem. The X2, t and F Distributions. Small and Large Sample Properties of Estimators and the Cramer-Rao lower bound inequality. Confidence interval for the mean of a population.


  1. The Maximum Likelihood Estimation Method.


Course Requirements


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.  


General Requirements

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.


Criteria for Determination of Grade


Active Participation 10%
Homework  10%
Midterm exam 35%
Final exam 45%



Grading scale follows the official UNYT as below:


Letter Grade Percent (%) Quality Points Generally Accepted Meaning
           A 96-100 4.00 Outstanding work
           A- 90-95 3.67
           B+ 87-89 3.33 Good work, distinctly above average
           B 83-86 3.00
           B- 80-82 2.67
           C+ 77-79 2.33 Acceptable work
           C 73-76 2.00
           C- 70-72 1.67
           D+ 67-69 1.33 Work that is significantly below average
           D 63-66 1.00
           D- 60-62 0.67
           F 0-59 0.00 Work that does not meet minimum standards for passing the course


Technology Expectations: usage of power-point, excel, word.  Students must keep copies of all assignments and projects sent by e-mail.

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 ( and/or the Academic Support Center, Dr. A Canollari ( 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.




Date Prepared: October 02/2015

Prepared by Prof. Dr. Fejzi Kolaneci



Faculty: Business &Economics.

Department: Maths & N.Sciences.

Grade: Undergraduate.

Majors: Computer Sciences.

Study Fileds: Computer Science.

Course Year: 2.

Course Program: UNYT.

Scheduele: MON 09-12:00

Instructor: Prof. Dr. Fejzi Kolaneci


Prerequisite: Calculus II