Information Package / Course Catalogue
Mathematical Statistics I
Course Code: EK203
Course Type: Required
Couse Group: First Cycle (Bachelor's Degree)
Education Language: Turkish
Work Placement: N/A
Theory: 3
Prt.: 0
Credit: 3
Lab: 0
ECTS: 5
Objectives of the Course

To gain the students the ability of expressing the basic concepts in statistical reliability in terms of mathematical expressions, distinguishing the probability distribution functions and density functions , comprehending the concepts related to hypothesis tests, the properties of the estimators, the basic principles concerning the theory of estimation, the transformations related with the functions of random variables , basic limit theorems and applying analysis of variance.

Course Content

Simple probability calculations, Random variable, sample space, probability distributions, distribution function, discrete and continuous functions, definitions and examples of probability density functions, Joint probability distributions, distribution and density functions, Marginal distribution and conditional functions, Concept of mathematical expectation, Concept of moment and usage of moment generating function, Limit theorems, Special probability distribution functions, Special probability density functions, Functions of random variables and transition techniques, Basic concepts related to estimation and properties of estimators, Basic concepts related to hypothesis testing and applications, Applications of analysis of variance.

Name of Lecturer(s)
Assoc. Prof. Elvan HAYAT
Learning Outcomes
1.To be able to express the concept of random variable.
2.To be able to express probability density and distribution functions.
3.To be able to distinguish special probability and density functions.
4.To be able to gain the main concepts related to estimation.
5. Calculating probabilities by probability functions of discrete and continuous random variables
Recommended or Required Reading
1.Freud, J.,E.,”Mathematical Statistics”
2.Larsen, R., J., Marx, M., L., “An Introduction to Mathematical Statistics and Its Applications”
Weekly Detailed Course Contents
Week 1 - Theoretical
Probability problems
Week 2 - Theoretical
Random variable, sample space, probability distributions, distribution function, discrete and continuous functions
Week 3 - Theoretical
Definitions of discrete and continuous probability distribution functions and examples
Week 4 - Theoretical
Joint probability distributions, distribution and density functions
Week 5 - Theoretical
Marginal distribution and conditional functions
Week 6 - Theoretical
Concept of mathematical expectation
Week 7 - Theoretical
Usage of moment generating function
Week 8 - Theoretical
Usage of moment generating function
Week 9 - Theoretical
Limit theorems
Week 10 - Theoretical
Special probability distribution functions
Week 11 - Theoretical
Special probability density functions
Week 12 - Theoretical
Functions of random variables and some probability calculations
Week 13 - Theoretical
Basic concepts related to estimation theory and estimators
Week 14 - Theoretical
Basic concepts related to hypothesis testing and applications
Assessment Methods and Criteria
Type of AssessmentCountPercent
Midterm Examination1%40
Final Examination1%70
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory142370
Individual Work72228
Midterm Examination110111
Final Examination115116
TOTAL WORKLOAD (hours)125
Contribution of Learning Outcomes to Programme Outcomes
PÇ-1
PÇ-2
PÇ-3
PÇ-4
PÇ-5
PÇ-6
PÇ-7
PÇ-8
PÇ-9
OÇ-1
4
5
4
5
4
5
4
4
4
OÇ-2
4
3
4
3
4
3
4
4
4
OÇ-3
4
3
4
3
4
3
4
3
4
OÇ-4
4
3
4
3
4
3
4
4
4
OÇ-5
Adnan Menderes University - Information Package / Course Catalogue
2026