Course Info
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Course Category
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Computer Science/Information Technology
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Course Level
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Graduate
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Credit Hours
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3
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Pre-requisites
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N/A
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Instructor
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Dr. Muhammad Akmal Butt
Ph.D
Georgia Institute of Technology, USA
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Course Contents
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Introduction to Probability and Stochastic Processes,
Set Theory,
Relations, Functions, Probability,
Probability; Experiments: Repeated, Dependent, Cascaded,
Joint Probability, Conditional Probability, Interesting Events, Total Probability,
Combinatronics, Birthday Problem, Bayes Rule,
Bayes Rule: Application, Partitioned Footpath, Partioned Floor,
Trains on a Junction, A local bus stop, Random line partition,
Equally likely outcomes, Random variables, Chuk-a-luck, Binomial & Poisson Distributions,
CDF of Poisson PMF, Joint Distribution: Example, Marginal PMF,
Conditional Distribution, Conditional PMF, Expected Value, Transformation of RV,
Conditional Expectation, Co-variance / Correlation,
Continuous Random Variable, Probability Density Function, PDF CDF of a Continuous RV,
CDF of a Continuous RV, CDF PDF of Nozzle Height, Exponential RV,
Failure of TV Set, Gaussian RV,
Mean of Transformed RV, Height Distribution of Humans, Higher Moments,
Scaling of Gaussian RV, Standard Gaussian Events, Joint Distributions,
Pair of RVs, Buffon's Needle, Exponential RV Pair, Pair of Erlang RVs
Exponential RV Pair, Pair of Dependent RVs,
Correlation & Covariance, Correlated Gaussian RVs,
Function of two RVs, Evaluation of Fz(Z), CDF / PDF of: Z = Y / X, Z = max (X, Y),
Multiple derived RVs, Probability Computation,
Pair of derived RVs
Direct computation of derived CDF,
Non-invertible Transformations,
Moments of U and V from f(x, y),
Expectation of transformed random variables, Covariance matrix, Eigenvalues & eigenvectors,
Vector RVs, Transforming Vector RVs,
PDF of Z = X+X ? 2X, Characteristic Functions,
Convergence of Sequence, Convergence of RVs,
Norm of Vectors and Function, Convergence of RV's, Inequalities,
Markov Chains
Markov Chains
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