PROBABILITY and RANDOM VARIABLES

AIM

This is a second year undergraduate course on introduction to probability and random variables. The course introduces fundamental differences between statistics and probability and then introduces basic topics of probability. Probability axioms, probability density functions, joint pdfs, and random variables with related topics are covered throughout the course. Heavy usage of computer simulations are performed so that the theory in class is verified via simulations.

CONTENT

This course contains; Class Info, Introduction to Statistics and Probability,Basic probability,Conditional probability,Discrete random variables,Discrete distributions and their statistics.,Continuous Random Variables and their statistics,Continuous Random Variables (Cont.),Midterm,Continuous Distributions,Multiple Discrete Random Variables,Multiple Continuous Random Variables,Conditional Probability Mass Functions,Conditional Probability Density Functions,Conditional Probability Density Functions.

1. 1

   Ability to simulate probability problems.

   Taught by: Problem Solving Method, Question - Answer Technique, Simulation Technique, Lecture Method · Assessed by: Traditional Written Exam, Homework

2. 2

   Ability to work with multiple random variables, their joint distributions, their conditional distributions, and their one and two dimensional transformations.

   Taught by: Problem Solving Method, Question - Answer Technique, Simulation Technique, Lecture Method · Assessed by: Traditional Written Exam, Homework

3. 3

   The ability to understand the common probability distributions and the understanding of where to use them. The ability to derive the statistics and other functions of the distribution.

   Taught by: Problem Solving Method, Question - Answer Technique, Simulation Technique, Lecture Method · Assessed by: Traditional Written Exam, Homework

4. 4

   The use of mathematical tools for discrete and continuous random variables

   Taught by: Problem Solving Method, Question - Answer Technique, Simulation Technique, Lecture Method · Assessed by: Traditional Written Exam, Homework

5. 5

   Calculate probabilities of events in a known event space, expected values, variances of random variables, and conditional probability.

   Taught by: Problem Solving Method, Question - Answer Technique, Simulation Technique, Lecture Method · Assessed by: Traditional Written Exam, Homework

6. 6

   Model simple probabilistic phenomena mathematically.

   Taught by: Problem Solving Method, Question - Answer Technique, Simulation Technique, Lecture Method · Assessed by: Traditional Written Exam, Homework

WEEKLY PLAN

1. WEEK 1

   Class Info, Introduction to Statistics and Probability

   Preparation: Syllabus, Text 1-Chap. 1, Text 2-Chap. 1 &2

2. WEEK 2

   Basic probability

   Preparation: Text 1-Chap. 2, Text 2-Chap 3

3. WEEK 3

   Conditional probability

   Preparation: Text 1-Chap. 2, Text 2-Chap 4

4. WEEK 4

   Discrete random variables

   Preparation: Text 1-Chap. 3, Text 2-Chap 5

5. WEEK 5

   Discrete distributions and their statistics.

   Preparation: Text 1-Chap. 3, Text 2-Chap 6

6. WEEK 6

   Continuous Random Variables and their statistics

   Preparation: Text 1-Chap. 4, Text 2-Chap 10

7. WEEK 7

   Continuous Random Variables (Cont.)

   Preparation: Text 1-Chap. 4, Text 2-Chap 10

8. WEEK 8

   Midterm

   Preparation: All Lectures till Week 8

9. WEEK 9

   Continuous Distributions

   Preparation: Text 1-Chap. 4, Text 2-Chap 11

10. WEEK 10

    Multiple Discrete Random Variables

    Preparation: Text 1-Chap. 5, Text 2-Chap 7

11. WEEK 11

    Multiple Continuous Random Variables

    Preparation: Text 1-Chap. 5, Text 2-Chap 12

12. WEEK 12

    Conditional Probability Mass Functions

    Preparation: Text 1-Chap. 5, Text 2-Chap 8

13. WEEK 13

    Conditional Probability Density Functions

    Preparation: Text 1-Chap. 5, Text 2-Chap 13

14. WEEK 14

    Conditional Probability Density Functions

    Preparation: Text 1-Chap. 5, Text 2-Chap 13

ASSESSMENT

• Rate of Midterm Exam to Success30%
• Rate of Final Exam to Success70%

WORKLOAD

READING

• 1. Applied Statistics and Probability for Engineers, Sixth Edition, Douglas C. Montgomery and George C. Runger, ISBN : 13 9781118539712 2. Intuitive Probability and Random Processes Using MatLab - Steven M. Kay, 2016, ISBN-13: 978-0-387-24157-9
• 1) A. Papoulis, Probability, Random Variables, and Stochastic Processes, Mc Graw Hill, 1984. 2) Alberto Leon-Garcia, Probability, Statistics, and Random Processes For Electrical Engineering, Prentice Hall, Third Edition, 2008. 3) A. Papoulis, Probability, Random Variables and Stochastic Processes, McGraw-Hill , Third Edition,1991

TEACHING STAFF

• Prof.Dr. Mehmet Kemal ÖZDEMİRCOORDINATOR
• Prof.Dr. Mehmet Kemal ÖZDEMİR
• Assist.Prof. Tuğba ASLAN KHALİFA
• Assoc.Prof. Mohamed Khaled Mohamed Ismaıl KHALIFA