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Introduction to Probability and Statistics
Course Code Semester
Course Name
LE/RC/LA
Course Type
Language of Instruction
ECTS
MBT1007
1
Introduction to Probability and Statistics
4/0/0
BSC
Turkish
6
Course Goals
Upon completion of this course, students are expected to understand and apply basic concepts in probability theory and mathematical statistics.
Prerequisite(s)
None
Corequisite(s)
None
Special Requisite(s)
The minimum qualifications that are expected from the students who want to attend the course.(Examples: Foreign language level, attendance, known theoretical pre-qualifications, etc.)
Instructor(s)
Assist. Prof. Dr. Uğur GÖNÜLLÜ
Course Assistant(s)
Schedule
Monday 09:00-11:00, Wedneday 11:00-13:00.
Office Hour(s)
Thursday 10:00-11:00, 3-A-15
Teaching Methods and Techniques
Lectures and recitation.
Principle Sources
I. Miller, M. Miller, John E. Freud’dan Matematiksel İstatistik (Çeviri: Ümit Şeneşen), Literatür Yayıncılık, 2002.
Other Sources
Sheldon M. Ross, OLASILIK ve İSTATİSTİĞE GİRİŞ -Mühendisler ve Fenciler için (Çeviri editörleri: Salih Çelebioğlu, Reşat Kasap), NOBEL Akademik Yayıncılık, 2015.
Seymour Lipschutz, Marc LIPSON, OLASILIK (Çeviri Editörü: Tahir Khaniyev), NOBEL Akademik Yayıncılık, 2013.
Course Schedules
Week
Contents
Learning Methods
1. Week
Sets, Combinatorial Methods, Binomial Coefficients
Lectures and recitation
2. Week
Sample Spaces, The Probability of an Event, Some Rules of Probability, Conditional Probability, Independent Event, Bayes' Theorem
Lectures and recitation
3. Week
Random Variables, Discrete Probability Distributions,
Lectures and recitation
4. Week
Continuous Random Variables, Multivariate Distributions,
Lectures and recitation
5. Week
Marginal Distributions,Conditional Distributions
Lectures and recitation
6. Week
The Expected Value of a Random Variable, Moments
Lectures and recitation
7. Week
Chebyshev’s Theorem, Moment Generating Functions, Product Moments, Conditional Expectation
Lectures and recitation
8. Week
The Discrete Uniform Distribution, The Bernoulli Distribution, The Binomial Distribution, The Negative Binomial and Geometric Distribution
Lectures and recitation
9. Week
The Hypergeometric Distribution, The Poisson Distribution
Lectures and recitation
10. Week
The Uniform Distribution, The Normal Distribution
Lectures and recitation
11. Week
The Normal Approximation to the Binomial Distribution, The Normal Approximation to the Poisson Distribution
Lectures and recitation
12. Week
Population and Sample. Statistical Inference,
Sampling With and Without Replacement
Lectures and recitation
13. Week
Random Samples,
The Sampling Distribution of the Mean,
The Sampling Distribution of the Mean: Finite Population
Lectures and recitation
14. Week
Interval Estimation
Lectures and recitation
15. Week
Final week
Exam
16. Week
Final week
Exam
17. Week
Final week
Exam
Assessments
Evaluation tools
Quantity
Weight(%)
Homework / Term Projects / Presentations
1
50
Final Exam
1
50
Program Outcomes
PO-1 Interpreting advanced theoretical and applied knowledge in Mathematics and Computer Science. PO-2 Critiquing and evaluating data by implementing the acquired knowledge and skills in Mathematics and Computer Science. PO-3 Recognizing, describing, and analyzing problems in Mathematics and Computer Science; producing solution proposals based on research and evidence. PO-4 Understanding the operating logic of computer and recognizing computational-based thinking using mathematics as a discipline. PO-5 Collaborating as a team-member, as well as individually, to produce solutions to problems in Mathematics and Computer Science. PO-6 Communicating in a foreign language, and interpreting oral and written communicational abilities in Turkish. PO-7 Using time effectively in inventing solutions by implementing analytical thinking. PO-8 Understanding professional ethics and responsibilities. PO-9 Having the ability to behave independently, to take initiative, and to be creative. PO-10 Understanding the importance of lifelong learning and developing professional skills continuously. PO-11 Using professional knowledge for the benefit of the society.
Learning Outcomes
LO-1 Compute permutations and combinations. LO-2 Understand what a random variable is. LO-3 Define basic probability terminology, e.g., experiment, outcome, sample space, event, etc. LO-4 Describe a probability distribution and a probability density function. LO-5 Understand mathematical expectation. LO-6 Explain joint, marginal and conditional probability distributions. LO-7 Understand where/when special probability distribution functions should be used. LO-8 Describe the various special continuous distributions. LO-9 Able to solve problems independently.
Course Assessment Matrix:
PO 1 PO 2 PO 3 PO 4 PO 5 PO 6 PO 7 PO 8 PO 9 PO 10 PO 11 LO 1 LO 2 LO 3 LO 4 LO 5 LO 6 LO 7 LO 8 LO 9