PROBABILITY and RANDOM VARIABLES

AIM

This is a second year undergraduate course (third year for CoE) 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.

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 overview,Continuous Distributions,Multiple Discrete Random Variables,Multiple Continuous Random Variables,Conditional Probability Mass Functions,Conditional Probability Density Functions,Conditional Probability Density Functions.

1. 1

   Model simple probabilistic phenomena mathematically.

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

2. 2

   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

3. 3

   Develops 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

4. 4

   Determines the common probability distributions and the understanding of where to use them.

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

5. 5

   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

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 overview

   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
• Assoc.Prof. Mohamed Khaled Mohamed Ismaıl KHALIFA
• Assist.Prof. Tuğba ASLAN KHALİFA