COURSE INFORMATION Course Title: PROBABILITY AND STATISTICS FOR ENGINEERS

Code	Course Type	Regular Semester	Theory	Practice	Lab	Credits	ECTS
MTH 205	A	3	2	2	0	3	5

Academic staff member responsible for the design of the course syllabus (name, surname, academic title/scientific degree, email address and signature)	NA
Lecturer (name, surname, academic title/scientific degree, email address and signature) and Office Hours:	Erind Bedalli
Second Lecturer(s) (name, surname, academic title/scientific degree, email address and signature) and Office Hours:	NA
Teaching Assistant(s) and Office Hours:	NA
Language:	English
Compulsory/Elective:	Compulsory
Classroom and Meeting Time:	A127 & A005
Course Description:	This course provides an elementary introduction to probability and statistics with applications. Descriptive statistics. Sets, events, and probability. Concept and definition of random variables and different functions of random variables. Both univariate and multivariate functions will be discussed. Discrete (binomial distribution, Poisson’s distribution) and continuous distribution functions (normal, lognormal, exponential distribution, gamma distribution), with the focus to commonly used probability distribution functions in civil engineering. Statistical estimation and testing; confidence intervals; and an introduction to linear regression. Statistics of extreme events. Testing of hypothesis. Engineering application.
Course Objectives:	The course will firstly introduce the concepts of finite probability theory and continuous probability theory. In the second part, the course addresses the statistical processes of formulating questions, collecting and analyzing data, and interpreting results. Methods related to descriptive and inferential statistics and the concept of probability are studied.

COURSE OUTLINE

Week	Topics
1	Introduction to probability.Random experiments, sample spaces and events. Axioms of probability.
2	Conditional probability. Multiplication and total probability rules. Independence. Bayes rule.
3	Discrete random variables. Probability mass function & cumulative distribution functions. Mean anc variance.
4	Probability distributions: uniform, binomial and geometric distributions. Their mean and variance.
5	Probability distributions: negative binomial, hypergeometric and Poisson distributions.
6	Continuous random variables. Probability density functions and cumulative distribution functions. Mean and variance.
7	Continuous probability distributions. The uniform and normal distribution.
8	Midterm exam.
9	The exponential distribution. Overview of lognormal, Erlang, Gamma and Weibull probability distributions.
10	Random sampling and data description.
11	Point estimation of parameters. Unbiased estimators. Estimators’ variance, std error. Sample distribution.
12	Statistical intervals for a single sample. Confidence intervals on the mean of normal distributions.
13	Hypothesis testing. Types of statistical hypothesis, one-sided and two-sided hypothesis.
14	Tests on the mean and variance of various distributions.

Prerequisite(s):
Textbook:	D. Montgomery, G.Runger , «Applied Statistics and Probability for Engineers»
Other References:
Laboratory Work:
Computer Usage:
Others:	No

COURSE LEARNING OUTCOMES

1	To comprehend and model various topics of probabilistic uncertainty that they will encounter in engineering scenarios.
2	To understand concepts of discrete probability, conditional probability, independence, and be able to apply these concepts to engineering applications
3	To be able to calculate the distribution function of a random variables and their means, variances and standard deviations.
4	To be able to properly organize and evaluate data.
5	Precaution and arrangement ability from statistical results.
6	Problem solve ability with theoretical and statistical techniques.

COURSE CONTRIBUTION TO... PROGRAM COMPETENCIES (Blank : no contribution, 1: least contribution ... 5: highest contribution)

No	Program Competencies	Cont.
Bachelor in Civil Engineering (3 years) Program
1	an ability to apply knowledge of mathematics, science, and engineering	5
2	an ability to design a system, component, or process to meet desired needs	5
3	an ability to function on multidisciplinary teams	5
4	an ability to identify, formulate, and solve engineering problems	5
5	an understanding of professional and ethical responsibility	4
6	an ability to communicate effectively	4
7	the broad education necessary to understand the impact of engineering solutions in a global and societal context	4
8	a recognition of the need for, and an ability to engage in life long learning	4
9	a knowledge of contemporary issues	4
10	an ability to use the techniques, skills, and modern engineering tools necessary for engineering practice	4
11	skills in project management and recognition of international standards and methodologies	4

COURSE EVALUATION METHOD

Method	Quantity	Percentage
Homework	2	7.5
Midterm Exam(s)	1	25
Quiz	2	7.5
Final Exam	1	40
Attendance		5
	Total Percent:	100%

ECTS (ALLOCATED BASED ON STUDENT WORKLOAD)

Activities	Quantity	Duration(Hours)	Total Workload(Hours)
Course Duration (Including the exam week: 16x Total course hours)	14	3	42
Hours for off-the-classroom study (Pre-study, practice)	14	3	42
Mid-terms	1	11	11
Assignments			0
Final examination	1	16	16
Other	1	14	14
Total Work Load:			125
Total Work Load/25(h):			5
ECTS Credit of the Course:			5