COURSE UNIT TITLE

: PROBABILITY AND STATISTICAL INFERENCE - II

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
STA 5056 PROBABILITY AND STATISTICAL INFERENCE - II COMPULSORY 3 0 0 9

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

PROFESSOR DOCTOR ÖZLEM EGE ORUÇ

Offered to

Statistics (English)
Statistics (English)
STATISTICS (ENGLISH)

Course Objective

The objective of this course is to provide a theoretical foundation for statistical inference. The three main goals in inference (estimation, confidence set construction and hypothesis testing) are discussed in inferential statistics framework.

Learning Outcomes of the Course Unit

1   Explain the concepts of random sample and statistics
2   Define the fundamental sampling distributions and its properties
3   Understand how to derive point estimators and their properties
4   Understand the theory behind confidence intervals
5   Understand the theory behind hypothesis testing and basic concepts of it (simple and composite hypotheses, rejection region, Type I and Type II error, power function, etc.)
6   Obtain the most powerful critical region for simple hypothesis
7   Obtain the likelihood ratio test critical region
8   Understand the theory behind sequential ratio probability test.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Random Samples,Sampling Distribution, Central limit theorem
2 Sampling Distributions(z and chi square)
3 Sampling Distributions(t and F)
4 Point Estimation, Point Estimation Methods (Method of Moments, Maximum Likelihood Method)
5 Properties of estimator (Bias and Variance; Mean-squared error)
6 Properties of estimator (Cramer-Rao inequality, efficiency, consistency and other asymptotic properties)
7 Sufficient statistics, exponential family
8 Interval Estimation and Pivotal Quantity
9 Confidence Interval Based on One-Sample
10 Confidence Interval Based on Two-Sample
11 Basic concepts of hypothesis testing (simple and composite hypotheses, rejection region, Type I and Type II error)
12 Hypothesis testing based on one-Sample and Two-Sample
13 Power function and power of the test, Most Powerful Test
14 Likelihood ratio test

Recomended or Required Reading

Textbook(s):
G.Casella and R.L:Berger, Statistical Inference, 2nd edition, Duxbury.
Supplementary Book(s):
1. R. V. Hogg and A.T.Craig, Introduction to Mathematical Statistics, 5th Edition, Prentice Hall
2. R. J. Larsen and M. L. Marx, An Introduction to Mathematical Statistics and Its Applications, 4th Edition, Prentice Hall.

Planned Learning Activities and Teaching Methods

The course consists of lecture, problem solving and homework.

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 ASG ASSIGNMENT
2 MTE MIDTERM EXAM
3 FIN FINAL EXAM
4 FCG FINAL COURSE GRADE ASG * 0.30 + MTE * 0.30 + FIN * 0.40
5 RST RESIT
6 FCGR FINAL COURSE GRADE (RESIT) ASG * 0.30 + MTE * 0.30 + RST * 0.40


Further Notes About Assessment Methods

None

Assessment Criteria

Final exam, midterm and homeworks.

Language of Instruction

English

Course Policies and Rules

Attendance is an essential requirement of this course and is the responsibility of the student. Any unethical behavior that occurs either in presentations or in exams will be dealt with as outlined in school policy. You can find the graduate policy at http://web.fbe.deu.edu.tr.

Contact Details for the Lecturer(s)

DEU Faculty of Sciences Department of Statistics
Prof.Dr.Özlem EGE ORUÇ
e-mail: ozlem.ege@deu.edu.tr
Tel: 0232 301 85 58

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 3 42
Preparations before/after weekly lectures 14 3 42
Preparation for final exam 1 60 60
Preparation for midterm exam 1 45 45
Preparing assignments 1 29 29
Final 1 2 2
Midterm 1 2 2
Project Assignment 1 3 3
TOTAL WORKLOAD (hours) 225

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10
LO.1555
LO.2555
LO.3555
LO.4555
LO.5555
LO.6555
LO.7555
LO.8555

CONTACT INFORMATION
Dokuz Eylül Üniversitesi Cumhuriyet Bulvarı No: 144 35210 Alsancak / İZMİR
Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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