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Campus
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MCS
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Programs
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PG
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Session
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Fall Semester 2016
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Course Title
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Stochastic Systems
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Course Code
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CSE-801
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Credit Hours
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3+0
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Pre-Requisutes
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An elementary course on probability theory
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Course Objectives
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Course Objective: The objective of this course is to prepare the students for a wide range of courses in communications, signal processing, image processing, control and other areas of engineering in which randomness has an important role.
Course
Learning Outcomes(CLOs)
CLO1: Review of probability theory, random variable, standard random variable, function of a random variable, Probability mass and density functions, Multiple Random variable, Binomial distribution, Multinomial distribution, poison distribution, Exponential distribution, Normal distribution, geometric distribution, Rayleigh distribution and other common distributions
CLO 2: Marginal distributions, Conditional distributions, Joint probability density functions, Conditional expected values, variances, moments, Covariance and correlation
CLO 3: Multivariate Normal distribution, Joint pdf, Random Process, The Bernoulli process, Poisson process, Poisson combining and splitting
CLO 4: Markov Process and Chains, Life death Process, random walk
CLO 5: Finite-state Markov chains; the matrix approach
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Detail Content
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- Review of probability theory, random variable, standard random variable, function of a random variable, Probability mass and density functions, Multiple Random variable, Binomial distribution, Multinomial distribution, poison distribution, Exponential distribution, Normal distribution, geometric distribution, Rayleigh distribution and other common distributions
- Marginal distributions, Conditional distributions, Joint probability density functions, Conditional expected values, variances, moments, Covariance and correlation
- Multivariate Normal distribution, Joint pdf, Random Process, The Bernoulli process, Poisson process, Poisson combining and splitting
- Markov Process and Chains, Life death Process, random walk
- Finite-state Markov chains; the matrix approach
- Hidden Markov chain, Viterbi Algorithm, Stationary, Ergodic and Cyclo-stationary Process,Weak and strong law of large numbers, Some useful inequalities
- Central limit theorem, Convergence in probability, Renewal process, Hypothesis testing and statistical decision theory, Bayesian Statistical Inference
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Text/Ref Books
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- Probability, Random Variables and Stochastic Processes, 4th edition by Athanasios Papoulis and S. Unnikrhmna.
- Introduction to Probability, 2nd edition, by Dimitri P. Bertsekas& John N. Tsitsiklis, MIT.
- Introduction to Probability Models, 10th edition, by Sheldon M. Ross.
- Viniotis, Y. (1998), Probability and Random Processes for Electrical Engineers, McGraw Hill, Boston.
- Hoel, Port and Stone, Introduction to Stochastic Processes
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Time Schedule
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Faculty/Resource Person
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Def Emp Col Dr Imran Touqir
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