Faculty: Faculty of Engineering

Department(s): IT, IE, MPA & PR

Course: Introduction to Probability and Statistics

Weekly hours: Theory: 2 Exercises: 2

ECTS Credits: 6

Lecture Schedule:

Monday - Lecture (classroom 106)

13:00-13:45

14:00-14:45

Friday - Exercise (classroom 106)

13:00-13:45

14:00-14:45

Lecturer: Asst. Prof. Dr. Hiqmet Kamberaj

Room Number: 409

Phone Number of the lecturer: +389 (0)23174010 (ext. 123)

E-mail address of the lecturer: km.ude.ubi|jarebmakh#km.ude.ubi|jarebmakh

Assistant: Asst. MSc Delcho Leskovski

Room Number: 408

Phone Number of the assistant: +389 (0)23174010 (ext. 138)

E-mail address of the assistant: km.ude.ubi|lohcled#km.ude.ubi|lohcled

**Course Objectives:**

The aim of the course is to give some basic terms, concepts, and learn how the stochastic methods come about and why they work. This course will provide students with a good understanding of the theory of probability, both discrete and continuous, including some combinatorics, a variety of useful distributions, expectation and variance, analysis of sample statistics, the law of large numbers, central limit theorem, confidence interval, testing hypotheses, t-test, and comparing two samples.

**Learning Outcomes:** (What the student should know and be able to do after completion of the course.

After completing this course, students will be able to:

- Develop the ability to solve problems using probability.
- Make connections between probability and other branches of mathematics.
- Understand the meaning of statistical statements as well as judge the quality of their content, when facing such problems on your own.
- Design and conduct experiments, as well as to analyze and interpret data

Skill outcomes | Neccessary ( + ) Not Neccessary ( –) |
---|---|

Written communication skills | + |

Oral communication skills | + |

Computer skills | + |

Working in laboratory | - |

Working team | + |

Preparing projects | + |

Knowledge of foreign language | + |

Scientific and professional literature analysis | + |

Problem solving skills | + |

Management skills | + |

Presentation skills | + |

**Course Textbooks:**

- H. Kamberaj, Probability and Statistics. Essentials about the probability and statistics., 2014.
- F.M. Dekking, C. Kraaikamp, H.P. Lopuhaä and L.E. Meester, A modern Introduction to Probability and Statistics. Understanding Why and How, Springer-Verlag, London, 2005 (ISBN 1852338962).
- M.R. Spiegel, J. Schiller and R.A. Srinivasan, Probability and Statistics, Third Edition, Schaum’s Outline Series, McGraw Hill, 2009 (ISBN 9780071544252).

Teaching methods | Ideal % |
---|---|

Teaching ex cathedra (teacher as the figure of authority, standing in front of the class and lecturing) | 85 |

Interactive teaching (ask questions in class, assign and check homework, or hold class or group discussions) | 8 |

Mentor teaching (consultant-teacher who has a supervisory responsibility and supervising the students) | - |

Laboratory work | - |

Seminar work | - |

Field Work (enables students to examine the theories and the practical experiences of a particular discipline interact) | - |

Semester project | 5 |

Case Study (An in-depth exploration of a particular context) | - |

Students Team work | 2 |

**Attendance:**

- Students are obliged to attend at least 10 weeks out of 14 weeks of lectures, exercises, and other activities (72%).
- The teaching staff should monitor and submit Course Attendance Report to the Student Affairs Office at the end of 14th week of each semester.
- The attendance rule for failed overlapping courses is %36 (5 weeks) and for non-overlapping courses is 57% (8 weeks);
- The attendance rule for course from upper semester is 57% (8 weeks).
- Students are not obliged to attend the course if the course is double repeated. However, they need to register and to pay repeated course.

**Exams (Mid-Term Exam, Final Exam, Make-up Exam):**

There are two exams, the Mid-Term and Final Exam, at the middle and at the end of the semester, respectively. The students, who do not earn minimum 50 credit points from the Mid-Term, Final Exam including Homework Assignments, have to take the Make-Up Exam, which counts only for Final Exam credit points. The terms of the exams are defined by the Academic Calendar announced on the University web site.

**Passing Score:**

The maximum number of credit points is collected during the semester, as follows: Mid-term Exam = 40 Credit Points (minimum requirement is 25 % to enter Final Exam), Final Exam (minimum requirement is 25 % to pass) = 40 Credit Points. Homeworks, quizzes, specific assignments and term papers = 20 Credit Points (minimum requirement is 5 credit points to enter Final Exam). Total=100.

**Weekly Study Plan**

Weeks | Topics |
---|---|

1 | Introduction to the philosophy of this course. Sets and Operations with Sets. Sample space and Events. Probability function definition: Joint and Disjoint Events. |

2 | Products of sample spaces. Conditional probability. |

3 | Multiplication rule, the law of total probability, Bayes’ rule and independence. |

4 | Discrete random variables (probability distributions). |

5 | Continuous random variables (probability distributions). |

6 | Expectation and Variance. |

7 | Mid term review. |

- | Mid Term Exam Week |

8 | Joint distributions and independence. Covariance and Correlation. |

9 | The law of large numbers and the central limit theorem. |

10 | Basics of statistical models. Data analysis. |

11 | The method of least squares. |

12 | Confidence intervals for the mean. |

13 | Testing hypotheses, t-test, and comparing two samples. |

14 | Final exam review. |

- | Final exam week. |

**Student workload:**

Please calculate the “Total Student Work Load” and then distribute that figure to the different engagements. For calculating the Total Student Work Load we multiply the course ECTS credits with standard figure 30. (ECTS Credit: 6) x 30 = 180 hours.

Activities | Hours |
---|---|

Lecture hours for 14 weeks: | 28 |

Laboratory and class exercises for 14 weeks: | 28 |

Student Mentoring for 14 weeks: | - |

Consultation for 14 weeks: | 4 |

Exam preparations and exam hours (Midterm, final, Makeups) Exam preparations and exam hours: Each one should be at least minimum 10 hours. | 30 |

Individual reading work for 14 weeks (Reading assignments/expectations for reading and comprehension is 5 pages per hour. Example: If a book 300 pages, total Individual reading work for 14 weeks 300:5 = 60 hours. | 50 |

Homework and work practice for 14 weeks: | 40 |

Preparation of diploma work, for 14 weeks: | - |