Probability and Stochastic Processes

By A. Gates Uncategorized
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About Course

Probability and Stochastic Processes.

Counting, elementary set theory, probability axioms, conditional probability, independence, discrete random variables, pmf, continuous random variables, CDF, pdf, moments, conditional distributions, functions of random variables, multiple random variables, jointly Gaussian vectors, probabilistic inequalities, laws of large numbers, central limit theorem, characteristic function, generating function and transform methods, stochastic processes, discrete-time processes, mean, autocorrelation, stationarity, cross-correlation, Poisson, Markov, Gaussian and Wiener processes, power spectral density, ergodicity, the response of linear systems to random signals


Course Content

Probability and Set Notation

  • Module 1 : Probability and Set Notation

Axioms of Probability and Conditional Probability

Random Variable Fundamentals

Moments of a Random Variable

Goodness of Fit Testing

Functions of a Random Variable

Jointly Distributed Random Variables

Working with Multiple Random Variables

Stochastic Processes

Stationarity & Ergodicity

Spectrum of a Random Signal

Stochastic Processes and LTI Systems

Markov Processes and Chains

Markov Process State Probabilities

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