Lecture_01_02_Intro_Probability_Theory

Lecture_01_02_Intro_Probability_Theory - Copyright © Syed...

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Unformatted text preview: Copyright © Syed Ali Khayam 2009 Analysis of Stochastic Systems Dr. Khawar Khurshid School of Electrical Engineering & Computer Science National University of Sciences & Technology (NUST) Copyright © Syed Ali Khayam 2008 Course Information b Lecture Timings: B Wednesdays: 5:30pm-6:20pm B Fridays: 5:30pm-7:20pm b Office Hours B Wednesday 6:20pm-7:20pm B khawar.khurshid@seecs.edu.pk b The course will be managed through LMS 2 Copyright © Syed Ali Khayam 2008 Textbook 3 Copyright © Syed Ali Khayam 2008 Course Outline b Syllabus B Introduction to Probability Theory B Random Variables B Limits and Inequalities B Stochastic Processes B Prediction and Estimation B Markov Chain and Processes (time permitting) 4 Copyright © Syed Ali Khayam 2008 Grading b Final Exam: 40% b Midterm Exam: 30% b Quizzes: 20% b Homework Assignments: 10% b Extra credit for extra effort 5 Copyright © Syed Ali Khayam 2008 Policies b Quizzes will be unannounced b Exams will be closed book, but you will be allowed to bring an A4-sized cheat sheet to the exam b Late homework submissions will not be accepted b Strong disciplinary action will be taken in case of plagiarism or cheating in exams, homework or quizzes b Attendance should be atleast 75% 6 Copyright © Syed Ali Khayam 2008 Why this course? b Stochastic theory is an extension of probability theory b This course on Stochastic theory will teach mathematical tools that are commonly-used in a variety of engineering, computer science and IT disciplines b We will focus mainly on the communications engineering aspects of the stochastic theory. b Applications and examples will be provided as required 7 Copyright © Syed Ali Khayam 2008 What will we cover in this lecture? b This lecture is intended to be an introduction to elementary probability theory b We will cover: B Random Experiments and Random Variables B Axioms of Probability B Mutual Exclusivity B Conditional Probability B Independence B Law of Total Probability B Bayes’ Theorem 8 Copyright © Syed Ali Khayam 2008 Definition of Probability b Probability: [m-w.org] 1 : the quality or state of being possible 2 : something (as an event or circumstance) that is possible 3 : the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes, the chance that a given event will occur 9 Copyright © Syed Ali Khayam 2008 Definition of Probability Do you know which famous scientist was so opposed to probability theory that he said: “ God does not play dice with the universe. ” And do you know which famous scientist said: “ God does play dice with the universe. All the evidence points to him being an inveterate gambler, who throws the dice on every possible occasion. ”?...
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Lecture_01_02_Intro_Probability_Theory - Copyright © Syed...

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