Course Name Code Semester T+U Hours Credit ECTS
Advanced Mathematical Statistics MAT 513 0 3 + 0 3 6
 Precondition Courses Students are assumed to be familiar with probability and mathematical statistics. Recommended Optional Courses Course Language Turkish Course Level yuksek_lisans Course Type Optional Course Coordinator Prof.Dr. ÖMER FARUK GÖZÜKIZIL Course Lecturers Course Assistants Course Category Course Objective To Understand the applications of probability and statistics in engineering and other applied sciences. Course Content Theory of distributions. Applications of Gamma and Betha Dist.,Moment generating functions and characteristic functions. Decision functions.Analysis of risk.Markov Chains. Regular probabilistic matrix. Canonical forms. Vector of probabilities.First passage probabilitiy. Inconsistent manner. First passage time.
# Course Learning Outcomes Teaching Methods Assessment Methods
1 to understand that applications of probability and statistics Lecture, Drilland Practice, Problem Solving, Testing, Homework,
2 to inference events. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
3 to analys of the data Lecture, Drilland Practice, Problem Solving, Testing, Homework,
4 to analys of risks and the functions of decision. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
5 to learn probabilities vector and its long time behaviour. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
6 to learn Markovian chains. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
Week Course Topics Preliminary Preparation
1 Theory of distributions.
2 Applications of Gamma and Betha Distributions
3 Weibull distribution and its applications
4 Moment generating functions
5 Characteristic functions
6 Distribution of the function to random variables
7 Decision , loss and risk functions.
8 Analysis of risk
9 Markov Chains
10 Regular probabilistic matrix and canonical forms.
11 Vector of probabilities and Ergodic chains
12 First passage probabilitiy
13 Inconsistent manner
14 First passage time
Resources
Course Notes
Course Resources Mathematical Statistics.Robert V.Hogg.1980.
Introductory Probability And Statistical Application ,Meyer, 1982
The Advanced Theory Of Statistics (Vol.1) Kendall, Stuart,1986.
Matematiksel İstatistik C.Cerit,1997.
Olasılık C.Cerit,2000.
Order Program Outcomes Level of Contribution
1 2 3 4 5
2 Student follows the current journals in his/her field and puts forward problems. X
2 Student follows the current journals in his/her field and puts forward problems. X
3 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
3 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
4 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
4 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
5 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
5 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
6 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
6 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
7 Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. X
7 Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. X
8 Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters X
8 Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters X
9 Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research. X
9 Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research. X
10 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. X
10 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. X
11 Student considers the scientific and cultural ethical values in the phases of gathering and conveying data or writing articles. X
Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 60
1. Kısa Sınav 10
2. Kısa Sınav 10
1. Ödev 20
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100