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Probability and Statistics

PİRİ REİS UNIVERSITY

GRADUATE SCHOOLS OF SCIENCE AND ENGINEERING

Computational Science and Engineering Programme

Course catalog Form

 

Course Name: MATH 624 Probability&Statistics

Degree:  PhD

 

Code

 

 

Year/Semester

 

Local Credits

 

ECTS Credits

 

Course Implementation, Hours/Week

Course

Tutorial

Laboratory

MATH 624

1/1 (spring)

3

7.5

3

-

-

Department

Computational Science and Engineering

Instructors

 

Dr. Duygu Nizamoğulları

Contact Information

 

E-mail: dnizamogullari@pirireis.edu.tr

Office Hours

 

Web page

http://www.pirireis.edu.tr

Course Type

 Compulsory

Course Language

English

Course Prerequisites

Elementary Calculus, Matrix Algebra.

Course Category by Content, %

Basic Sciences

Engineering Science

Engineering Design

Humanities

60

20

20

 

Course Description

Topics in probability include discrete and continuous  random variables, probability distributions, sums and  functions of random variables. Topics in statistics include sample mean and variance, distributions, regression and hypothesis testing.

 

Course Objectives

 

This course is designed for engineering students to enrich them in probability theory and  to use of probability tools for statistical inference in engineering problems.

 

Course Learning Outcomes

 

Upon succesful completion of the course students are expected to

  1. calculate and interpret descriptive statistics
  2.  know probability theory for both discrete and continuous random variables.
  3.  know many applications of probability theory
  4. learn how to use probability theory for many problems
  5. use probability theory they will able to make statistical inference for many engineering problems
  6. know fundamental statistical concepts.
  7. be able to select the appropriate statistical methods depending on the type of data.

 

Instructional Methods and Techniques

Books, lecture notes and problem solving.

Tutorial Place

Class

Co-term Condition

 

Textbook

Probability and Statistics for Engineers and scientists, R.E. Walpole, R.H. Myers, S. L. Myers, K. Ye, Seventh Edition; Prentice Hall

 

Other References

· Mathematical Statistics, I. Miller, M. Miller, Sixth Edition; Prentice Hall

· A First Course in Probability, S. Ross, Fifth Edition; Prentice Hall

 

Homework & Projects

Homework assignments based on lectures will be given regularly

Laboratory Work

 

Computer Use

 

Other Activities

The weekly coverage may change as it depends on the progress

                   

 

Assessment Criteria

Activities

Quantity

Effects on Grading, %

Attendance

 

 

Midterm

1

30

Quiz

 

 

Homework

3

10

Term Paper/Project

 

 

Laboratory Work

 

 

Practices

 

 

Tutorial

 

 

Seminar

 

 

Presentation

1

10

Field Study

 

 

Final Exam

1

50

TOTAL

 

100

Effects of Midterm on Grading, %

 

50

Effects of Final on Grading, %

 

50

TOTAL

 

100

 

ECTS/

WORKLOAD TABLE

Activities

Count

Hours

Total Workload

Lecture

14

3

42

Midterm

1

50

50

Quiz

3

5

15

Homework

 

 

 

Term Paper/Project

 

 

 

Laboratory Work

 

 

 

Practices

 

 

 

Tutorial

 

 

 

Seminar

 

 

 

Presentation

1

30

30

Field Study

 

 

 

Final Exam

1

50

50

Total Workload

 

 

187

Total Workload/25

 

 

 

Course ECTS Credits

 

 

7,5

 

 

Week

 

Topics

Course Outcomes

1

Review of some Combinatorics: The Basic principle of Counting, Permutations, Combinations, Binomial Coefficients.

Statistical Inference, The role of Probability, The Sample Mean, Measures of Variability, Discrete and Continuous Data, Graphical Methods and Data Description.

I

2

Sample space, Events, Probability of an Event, Some Rules of Probability

I-II

3

Conditional Probability, Independent Events, Baye’s Rule

II-III

4

Concept of a Random Variable, Discrete Probability Distributions, Continuous Probability Distributions.

II-III

5

Joint Probability Distributions, Conditional Probability Distributions, Probability Density Functions.

II-III

6

Expected value of a Random Variable, Variance and Covariance.

II-III-IV

7

Expected Values and Variances of Linear combinations of Random Variables, Chebyhev’s Theorem, Moments Generating Functions, Conditional Expectations.

II-III-IV

8

MIDTERM

 

9

Discrete Uniform Distribution, Binomial and Multinomial Distributions, Negative Binomial and Geometric Distributions, Poisson Distribution.

II-III-IV

10

Continuous Uniform Distribution, Normal Distribution, Gamma and Exponential Distributions, Chi-squared Distribution.

II-III-IV

11

Random Sampling, Some Important Statistics, Sampling Distributions, t-distribution, F-distribution.

III-IV-V

12

Distributions of Sampling Statistics, Parameter Estimation

V-VI

13

Statistical Hypotheses: General Concepts, Testing a Statistical Hypotheses

VI-VII

14

Regression Analysis

VI-VII

 

Relationship between the Course and the Computational Science and Engineering Curriculum

 

 

Program Outcomes

Level of Contribution

1

2

3

a

Understands and applies basic sciences, mathematics and engineering sciences at a high level.

 

 

 

X

b

Has extensive and in-depth knowledge of the field, including the latest developments.

 

 

X

 

c

Gets the latest information in the area and has a high level of competence in the methods and skills necessary to understand it.

 

 

X

 

d

Makes a comprehensive study which develops a new scientific method or technological product / process that brings innovation to technology or technology, or applies a known method to a new field.

 

 

X

 

e

Perceives, designs, implements and finalizes an original research process  and manages  this  independently.

X

 

 

f

Contributes to the scientific and technological literature by publishing the outputs of academic studies in respectable academic environments.

 

 

X

 

g

Conveys scientific, technological, social and cultural developments  with the consciousness of scientific impartiality and ethical responsibility.

 

X

 

 

h

Understanding of the theoretical basis of computer science to identify, formulate, and solve progressively more challenging computational science problems

 

X

 

 

i

Ability to design and implement a computer-based system or develop a program to meet the criteria in industry

 

X

 

 

 

         1: Small, 2: Partial, 3: Full

 

Prepared by

 

Dr. Duygu NİZAMOĞULLARI

Date

 

26/04/2018

Signature