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CENG 381

Stochastic Processes

Prerequisites:

Probability spaces, random variables, distribution and density functions, random vectors, sequences of random variables, convergence notions, the central limit theorem, the law of large numbers, stochastic processes, stationary notions, Poisson processes, Gaussian processes, transformations of stochastic processes, ergodicity, second order random processes, representation theorems, Markov processes, homogeneous Markov models and applications.

Topics
Introduction
Quick Review of Probability
Random Variables, Parameters of Random Variables, Jointly Distributed Random Variables
Transform Methods, Moment Generating Function, Inequalities
Probability Distributions – Discrete Random Variables
Probability Distributions – Discrete RV s, Continuous RV s
Probability Distributions – Continuous Random Variables – Central Limit Theorem, Applied Transforms
Midterm
Stochastic Processes, Poisson Process
Birth+Death Process
Markov Chains
Queueing Theory, Introduction, Describing a Queueing System
Little s Law, M/M/1 Queueing System
Other Queueing Systems