MATHEMATICAL STATISTICS

Course Code:

MATH 462

Course Type:

Area Elective

P:

3

Lab:

0

Laboratuvar Saati:

0

Credits:

3

ECTS:

7

Course Language:

English

Course Objectives:

To prepare students for a career in actuarial science, graduate studies in financial engineering/mathematics and high school teachers to teach probability and statistics in high schools.

Course Content:

Introduction and background. Populations and samples. Measures of the center of a set of observations. Measurement of variability. Sampling, sampling distributions. Estimations. Hypothesis testing. Statistical decision theory. Contigency Tables. Regression and correlation analysis.

Course Methodology:

1: Lecture, 2: Problem Solving

Course Evaluation Methods:

A: Written examination, B: Homework

Vertical Tabs

Course Learning Outcomes

Learning Outcomes	Program Learning Outcomes	Teaching Methods	Assessment Methods
1) Compute measures od central tendency	3,4,5,6,7,8,9	1,2	A,B
2) Compute measures of variability	3,4,5,6,7,8,9	1,2	A,B
3) Estimate parameters of a distribution	3,4,5,6,7,8,9	1,2	A,B
4) Perform hypothesis testing	3,4,5,6,7,8,9	1,2	A,B
5) Apply contigency tables	3,4,5,6,7,8,9	1,2	A,B
6) Use regression equations	3,4,5,6,7,8,9	1,2	A,B

Course Flow

Week	Topics	Study Materials
1	Descriptive Statistics. Histograms, measures of Central Tendency and Dispersion.
2	Estimating Parameters: the method of Maximum Likelihood and the Method of Moments.
3	Properties of Estimators: Unbiased, Minimum Variance Estimators
4	The Rao- Cramer Inequality. Efficiency, Sufficiency, Consistency.
5	Hypothesis testing concerning the Mean of the Normal Distribution. Null and Alternative Hypothesis. Type I and II Errors.
6	Critical Point, Test Statistic, One Tail and Two Tail Tests when σ is Known.
7	P-value. Small sample T-test. Power of Test.
8	Relation between Type I error, Type II error and sample size. Test concerning the parameter p of the Binomial distribution.
9	Confidence intervals concerning μ and p. Determining the sample size.
10	Paired t-test, tests concerning the means of two populations. Test concerning a single variance. Test concerning two variances.
11	Hypothesis testing concerning non-normal data. The likelihood ratio test.
12	The Multinomial Distribution Goodness-of-Fit Tests: All Parameters Known.
13	Contingency Tables. Regression Analysis
14	Regressions Analysis. The Method of Least Squares. The Linear Model. Covariance and Correlation.

Recommended Sources

Textbook	Mathematical Statistics with Applicatins. Wackerly, Mendenhall, Scheaffer. Brooks/Cole
Additional Resources

Material Sharing

Documents	Yulearn
Assignments	Homework sets
Exams

Assessment

IN-TERM STUDIES	NUMBER	PERCENTAGE
Mid-terms	1	57
Quizzes
Assignments	3	43
Total		100
CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE		50
CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE		50
Total		100

Course’s Contribution to Program

No	Program Learning Outcomes	Contribution
No	Program Learning Outcomes	1	2	3	4	5
1	The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamenral research fields in mathematics (i.e., analysis, algebra, differential equations and geometry)					x
2	Acquiring fundamental knowledge on fundamental research fields in mathematics					x
3	Ability form and interpret the relations between research topics in mathematics			x
4	Ability to define, formulate and solve mathmatical problems					x
5	Consciousness of professional ethics and responsibilty		x
6	Ability to communicate actively			x
7	Ability of self-development in fields of interest			x
8	Ability to learn, choose and use necessary information technologies			x
9	Lifelong education				x

ECTS

IN-TERM STUDIES	NUMBER	PERCENTAGE
Mid-terms	1	57
Quizzes
Assignments	3	43
Total		100
CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE		50
CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE		50
Total		100

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