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Introduction to Stochastic Processes: Course Overview and Key Concepts

This introductory lecture by Sajjad Hussain on Stochastic Processes provides a foundational understanding essential for various applications, such as signal processing, wireless communications, and computer network traffic analysis. Highlighting the importance of statistical methods like the Binomial and Poisson distributions, the course addresses how randomness affects data communication reliability and models like Markov Chains that influence traffic predictions. Engaging mathematical puzzles from Gardner's work complement the learning experience, ensuring students grasp critical concepts necessary for real-world applications.

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Introduction to Stochastic Processes: Course Overview and Key Concepts

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Presentation Transcript

  1. Stochastic ProcessesIntroductory Lecture SajjadHussain

  2. Why should I study this course… [1] • Signal Processing ???

  3. Why should I study this course… [2] • Computer Memories • To make the system reliable we store k+l bits instead of k original bits • At least how many bits out of k+l bits read correctly would suffice the correct data reading • Binomial Random Variable shall provide the answer. • Optical Communication Systems • Photo detector converts light into electrical energy. • Photoelectrons produced are well modeled by Poisson Random Variable.

  4. Why should I study this course…[3] • Wireless Communications • Thermal noise modeled as Gaussian Random Variable • Rayleigh, Rician, Chi-squared distributions to model different wireless channels • Computer Network Traffic • LANs, WANs, www traffic can be linked to Markov Chains • Studies have produced surprising insights into buffer size, congestion control, connection duration prediction etc. BUT…

  5. Reading Assignment: Entertaining Mathematical Puzzles [Gardner, 1986]

  6. A road map for the text Experiments, Models, Probabilities Discrete RV Continuous RV Pairs of Random Variables Random Vectors 6. Sums of RVs 7. Parameter Estimation using the sample mean 8. Hypothesis Testing 9. Estimation of a RV 10. Stochastic Processes 12. Markov Chain 10. Stochastic Processes 11. Random Signal Processing

  7. Couple of announcement: • Class starts at 17h45 on Thursdays to accommodate a 15 minute break for Maghrib Prayers • Need a volunteer to represent/coordinate the class

  8. Teaser - 1

  9. Teaser – 2Who wants to be a millionaire… • Would you prefer to omit two wrong options out of four or you would like try twice to answer the question with four options?

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