Information Package / Course Catalogue
Mathematical Statistics II
Course Code: EK204
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
Basic consepts for statistical inference
Week 2 - Theoretical
The basic consepts of estimators, the four properties of estimators: unbiasedness, minimum variance, sufficiency, efficiency
Week 3 - Theoretical
The method of moments in estimation
Week 4 - Theoretical
The maximum likelihood methods in estimation
Week 5 - Theoretical
Familiar with the method of moments estimator for discrete and continuous distributions to obtain
Week 6 - Theoretical
Familiar with the method of maximum likelihood methods for discrete and continuous distributions to obtain
Week 7 - Theoretical
Comparisions of moments method and maximum likelihood methods
Week 8 - Theoretical
Comparisions of moments method and maximum likelihood methods
Week 9 - Theoretical
Hypothesis Testing Theory
Week 10 - Theoretical
Calculation of power of test
Week 11 - Theoretical
Likelihood Ratio Test
Week 12 - Theoretical
Neyman-Pearson lemma
Week 13 - Theoretical
Neyman-Pearson lemma
Week 14 - Theoretical
Order Statistics and the distributions of order statistics
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
3
4
3
4
3
4
4
4
OÇ-2
4
5
4
5
3
4
3
4
3
OÇ-3
4
3
4
3
4
3
4
3
4
OÇ-4
4
3
4
3
4
3
4
3
4
OÇ-5
Adnan Menderes University - Information Package / Course Catalogue
2026