| MATHEMATICS | |||||
| Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 | ||
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT3026 | Probability and Statistics | Spring | 3 | 0 | 3 | 6 |
| Language of instruction: | English |
| Type of course: | Must Course |
| Course Level: | Bachelor’s Degree (First Cycle) |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Instructor NERMINE AHMED EL SISSI |
| Course Lecturer(s): |
Dr. Öğr. Üyesi MÜRÜVVET ASLI AYDIN |
| Recommended Optional Program Components: | None |
| Course Objectives: | Topics in probability and statistics are introduced through their definitions leading to the development of basic probabilistic and statistical tools. Emphasis is placed on using these tools to solve engineering problems and to make informed decisions. |
|
The students who have succeeded in this course; 1) Calculate probability using permutations and combinations 2) Calculate probability of unions and intersects 3) Determine the reliability block diagram of a system of elements 4) Understand the conditional probability an apply on probability problems 5) Calculate probability using probability distribution functions 6) Calculate expectation values 7) Apply hypothesis testing 8) Determine confidence intervals |
| The course will cover the following topics: Counting and probability (both theoretical and experimental definitions); Rules of probability (based on set theory); conditional probability; The random variable; probability mass functions and density functions; Expectation values; sampling theory (mean and standard deviation); hypothesis testing; Confidence intervals (for the population mean, population standard deviation). |
| Week | Subject | Related Preparation |
| 1) | Introduction to the course. | |
| 2) | Counting and probability. | |
| 3) | Rules of Probability (sets, additive rules, independence), the Reliability Block Diagram. | |
| 4) | Conditional probability (independence, Bayes' theory). | |
| 5) | The random variable, and probability distributions (discrete and continuous) \ review. | |
| 6) | Expectation values: the population mean. | |
| 7) | Expectation values: the population standard deviation. | |
| 8) | Special discrete distributions (Geometric, Hypergeometric, Binomial, Poisson). | |
| 9) | Special continuous distributions (Exponential, Weibull, Normal). | |
| 10) | Sampling (the sampled mean and standard deviation, and their distributions) \ review. | |
| 11) | Hypothesis testing (p-values for the mean and standard deviation, t- and chi-square-distributions). | |
| 12) | Confidence intervals I - intervals for the mean, pairing, standard error in the sample mean. | |
| 13) | Confidence intervals II - intervals for the mean (two population) | |
| 14) | Confidence intervals III - intervals for the standard deviation. |
| Course Notes / Textbooks: | Walpole, Ronald E., et al. "Probability & Statistics for Engineers & Scientists", Prentice Hall, 9th ed. |
| References: | Douglas C. Montgomery & George C. Runger. "Applied Statistics and Probability for Engineers”; (2011) Wiley. Devore, Jay.; "Probability & Statistics for Engineering and the Sciences". CengageBrain.com. |
| Semester Requirements | Number of Activities | Level of Contribution |
| Midterms | 2 | % 60 |
| Final | 1 | % 40 |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 60 | |
| PERCENTAGE OF FINAL WORK | % 40 | |
| Total | % 100 | |
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Study Hours Out of Class | 14 | 7 | 98 |
| Midterms | 1 | 2 | 2 |
| Final | 1 | 2 | 2 |
| Total Workload | 144 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution | |
| 1) | To have a grasp of basic mathematics, applied mathematics and theories and applications in Mathematics | 5 |
| 2) | To be able to understand and assess mathematical proofs and construct appropriate proofs of their own and also define and analyze problems and to find solutions based on scientific methods, | 5 |
| 3) | To be able to apply mathematics in real life with interdisciplinary approach and to discover their potentials, | 4 |
| 4) | To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself, | 4 |
| 5) | To be able to tell theoretical and technical information easily to both experts in detail and non-experts in basic and comprehensible way, | 4 |
| 6) | To be familiar with computer programs used in the fields of mathematics and to be able to use at least one of them effectively at the European Computer Driving Licence Advanced Level, | 4 |
| 7) | To be able to behave in accordance with social, scientific and ethical values in each step of the projects involved and to be able to introduce and apply projects in terms of civic engagement, | |
| 8) | To be able to evaluate all processes effectively and to have enough awareness about quality management by being conscious and having intellectual background in the universal sense, | 3 |
| 9) | By having a way of abstract thinking, to be able to connect concrete events and to transfer solutions, to be able to design experiments, collect data, and analyze results by scientific methods and to interfere, | |
| 10) | To be able to continue lifelong learning by renewing the knowledge, the abilities and the competencies which have been developed during the program, and being conscious about lifelong learning, | 3 |
| 11) | To be able to adapt and transfer the knowledge gained in the areas of mathematics ; such as algebra, analysis, number theory, mathematical logic, geometry and topology to the level of secondary school, | 3 |
| 12) | To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively. | 4 |