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Syllabus ( MATH 308 )


   Basic information
Course title: Probability Theory
Course code: MATH 308
Lecturer: Assist. Prof. Hadi ALIZADEH
ECTS credits: 6
GTU credits: 3 (3+0+0)
Year, Semester: 3, Spring
Level of course: First Cycle (Undergraduate)
Type of course: Compulsory
Language of instruction: English
Mode of delivery: Face to face
Pre- and co-requisites: None
Professional practice: No
Purpose of the course: This course is designed to provide the student with a solid background and understanding of the basic results and methods in probability theory needed in more advanced courses in probability, mathematical statistics and related subjects.
   Learning outcomes Up

Upon successful completion of this course, students will be able to:

  1. construct a solid background and understanding of the basic results and methods in probability theory needed in more advanced courses in probability, mathematical statistics and related subjects.

    Contribution to Program Outcomes

    1. Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.

    Method of assessment

    1. Written exam
  2. explain the concept of probability space, probability measures, sample space, algebra of events; s-algebra of events.

    Contribution to Program Outcomes

    1. Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
    2. Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.

    Method of assessment

    1. Written exam
  3. explain the concepts of distribution functions, discrete and continuous probability space.

    Contribution to Program Outcomes

    1. Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.
    2. Exhibiting professional and ethical responsibility.

    Method of assessment

    1. Written exam
  4. perceive the idea of random variables, Independency of random variables and their distributions;.

    Contribution to Program Outcomes

    1. Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
    2. Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.
    3. Exhibiting professional and ethical responsibility.

    Method of assessment

    1. Written exam
    2. Homework assignment
  5. explain tle subject of expectation, characteristic function and how to obtain the moments of a distribution function.

    Contribution to Program Outcomes

    1. Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.

    Method of assessment

    1. Homework assignment
  6. gain the capability of using some inequalities and limit theorems.

    Contribution to Program Outcomes

    1. Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.

    Method of assessment

    1. Homework assignment
   Contents Up
Week 1: Probability; sample space; algebra of events; s-algebra of events.
Week 2: probability measure on a s-algebra; algebra of borel sets; Kolmogorov axioms.
Week 3: equivalency of additivity axioms and continuity for probability.
Week 4: Discrete sample; probabilities in discrete sample space; equally likely outcomes.
Week 5: Distribution functions; extension of measure defined on algebra of intervals to algebra of borel sets;
Week 6: one to one mapping between probability measure and distribution functions; examples of discrete and continuous probability space.
Week 7: Random variables, random vectors and their distributions;
Week 8: Midterm exam 1 and solutions
Week 9: Functions of random variables; s-field generated by a random variable.
Week 10: Conditional probability, definition of Lebesgue integral and variance of a random variable.
Week 11: Expectation and characteristic function.
Week 12: Midterm exam 2; computation of moments using characteristic function.
Week 13: Definition of correlation and covariance; Chebyshev’s inequalities. Law of large numbers; Limit theorems;
Week 14: Continuity theorem of characteristic function; Central limit theorem; Strong law of large numbers.
Week 15*: -
Week 16*: Final exam
Textbooks and materials: A First Couse in Probability. Ross S. Prentice Hall Inc.
Recommended readings: Introduction to the Theory of Statistics. Mood A.M., Graybill F. A., Boes D.C.
Introduction to Mathematical Statistics. New York: Macmillan. R.V. Hogg and A.T. Craig.
  * Between 15th and 16th weeks is there a free week for students to prepare for final exam.
Assessment Up
Method of assessment Week number Weight (%)
Mid-terms: 8, 12 35
Other in-term studies: 0
Project: 0
Homework: 1,2,3,4,5 5
Quiz: 0
Final exam: 16 60
  Total weight:
(%)
   Workload Up
Activity Duration (Hours per week) Total number of weeks Total hours in term
Courses (Face-to-face teaching): 3 14
Own studies outside class: 4 14
Practice, Recitation: 0 0
Homework: 4 5
Term project: 0 0
Term project presentation: 0 0
Quiz: 0 0
Own study for mid-term exam: 8 2
Mid-term: 4 2
Personal studies for final exam: 10 1
Final exam: 2 1
    Total workload:
    Total ECTS credits:
*
  * ECTS credit is calculated by dividing total workload by 25.
(1 ECTS = 25 work hours)
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