• Basic information
• Learning outcomes
• Contents
• Assessment
• Workload

Learning outcomes

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
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:	1-1 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:	Distribution functions of discrete and continuous random variables. Midterm Exam - 1.
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:	Computation of moments using characteristic function. Midterm Exam - 2.
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
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
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)