Iğdır University Lifelong Learning Programme

Description of Individual Course Units

Course Unit Code	Course Unit Title	Type of Course Unit	Year of Study	Semester	Number of ECTS Credits
170300401406	PROBABILITY and STATISTICS II	Compulsory	2	4	5

Level of Course Unit

First Cycle

Objectives of the Course

Understanding and interpreting basic mathematical statistical concepts, and linking theory with practice

Name of Lecturer(s)

Prof. Dr. Elman HAZAR

Learning Outcomes

1	Understand required definitions for statistical inference, (Difference of population and sample concepts, definition of parameter)
2	Define the concepts of statistics and estimator (point estimator, interval estimator)
3	Apply estimating methods (moments, least squares, maximum likelihood, bayes estimation methods)
4	Expresses the required characteristics (unbiasedness, consistency, efficiency, sufficiency, minimum variance, etc.) sought in the estimators
5	Obtain interval estimate for the population parameter (parameters)
6	The hypothesis testing in accordance with the theory of the parametric statistical inference for the population parameter (parameters)

Mode of Delivery

Daytime Class

Prerequisites and co-requisities

Recommended Optional Programme Components

Course Contents

Examination of statistical properties of estimators obtained according to sample and sample statistics. Determination of statistical inference about the parameter estimation. Hypothesis test for the parameters.

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Concepts of population, parameter and sample. Sampling Distributions
2	Asymptotic properties of estimators, convergence in probability (large numbers law), convergence in distribution (central limit theorem), convergence in moments.
3	Order statistics and some statistics related to them (mod, median, percentile, etc.)
4	Introduction to parameter estimation problem
5	Required qualifications of estimators: unbiasedness, sufficiency
6	Consistency, efficiency, completeness
7	Best unbiased estimators, Cramer-Rao inequality
8	Midterm
9	Rao-Blackwell theorem, Lehmann-Scheffe uniqueness theorem
10	Distribution properties of estimators (obtain asymptotic distributions with Taylor series and some properties)
11	Introduction to hypothesis test problem: definition of hypothesis testing, simple and complex hypothesis, test function
12	Error probabilities and Power functions, Most powerful tests
13	Likelihood ratio tests and Neymann-Pearson test
14	Applications of Neymann-Pearson lemma, testing of complex hypotheses
15	Final Exam

Recommended or Required Reading

Akdi, Y.(2014), Matematiksel İstatistiğe Giriş, Gazi Kitabevi 4.Baskı (Ders kitabı) Casella, G. (2001). Statistical Inference. Pacific Grove, Calif. : Wadsworth. Hogg, Robert, V., Craig, Allan, T. (1978). Introduction to Mathematical Statistics. 4 nd ed., New York: Macmillan. Wackerly,D. Dennis, Mendenhall,William, Scheaffer, Richard (2002) Mathematical Statistics with Applications. 6th Ed. California, Duxbury.

Planned Learning Activities and Teaching Methods

Assessment Methods and Criteria

Term (or Year) Learning Activities	Quantity	Weight
Midterm Examination	1	100
SUM		100
End Of Term (or Year) Learning Activities	Quantity	Weight
Final Examination	1	100
SUM		100
Term (or Year) Learning Activities		40
End Of Term (or Year) Learning Activities		60
SUM		100

Language of Instruction

Turkish

Work Placement(s)

Workload Calculation

Activities	Number	Time (hours)	Total Work Load (hours)
Midterm Examination	1	1	1
Final Examination	1	2	2
Attending Lectures	14	3	42
Question-Answer	14	3	42
Individual Study for Mid term Examination	1	20	20
Individual Study for Final Examination	1	30	30
TOTAL WORKLOAD (hours)			137

Contribution of Learning Outcomes to Programme Outcomes

	PO 1	PO 2	PO 3	PO 4	PO 5	PO 6	PO 7	PO 8	PO 9	PO 10
LO1	4	4	4	4	4	4	4	4	4	4
LO2	4	4	4	4	4	4	4	4	4	4
LO3	4	4	4	4	4	4	4	4	4	4
LO4	4	4	4	4	4	4	4	4	4	4
LO5	4	4	4	4	4	4	4	4	4	4
LO6	4	4	4	4	4	4	4	4	4	4

* Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High