EECS 422: Random Processes in Communications and Control I

Winter 2013

Lecture 1 | Introduction, Probability spaces, properties of probability measures, conditional probability, independence. |

Lecture 2 | Bayes' rule and inference, independent trials, discrete random variables and probability mass functions, cumulative distribution functions, continuous random variables and densities. |

Lecture 3 | Mixed and singular random variables, conditional distributions, functions of random variables, expected values. |

Lecture 4 | Moments, Gaussian random variables, Markov's inequality, Chebyshev's inequality, Chernoff bounds, Moment Generating Functions. |

Lecture 5 | Random vectors, joint cdfs, pdfs and pmfs, marginal distributions, independence. |

Lecture 6 | Conditional Distributions, functions of multiple random variables, sums of random variables, characteristic functions, linear transformations of random vectors, expectation and moments of random vectors, correlation and covariance. |

Lecture 7 | Correlation coeeficients, jointly Gaussian random variables, Gaussian Random variables and linear transformations. |

Lecture 8 | Covariance matrices, conditioning and jointly Gaussian Random variables, conditional expectation, iterated expectation, introduction to estimation. |

Lecture 9 | Baysian MMSE estimation, estimation and jointly Gaussian random variables, LLSE estimation. |

Lecture 10 | Orthogonality property of MMSE estimates, Discrete-time random processes, i.i.d. processes and laws of large numbers, mean square convergence, convergence in probability, Almost sure convergence. |

MID-TERM EXAM | |

Lecture 11 | Convergence in distribution, the central limit theorem. |

Lecture 12 | Finite dimensional distributions and Kolmogorov's theorem, Stationary processes, memoryless processes, stationary increments, independent increments, Markov property, counting processes, random walks. |

Lecture 13 | Markov chains: transition matrices/graphs, n-step transistions, first-step analysis. |

Lecture 14 | Markov chains: state classification, stationary distribtuions. |

Lecture 15 | Arrival processes/counting processes, Poisson processes. |

Lecture 16 | Mean and correlation/covariance functions, wide sense stationary processes, Gaussian Processes, Wiener processes. |

Lecture 17 | Multiple random processes, cross correlation functions, Mean-square calculus. |

Lecture 18 | Mean-square integration, random processes and linear systems, power spectral density functions. |

Lecture 19 | Systems driven by white noise; optimal linear filtering; the non-causal Wiener filter; overview of related courses. |

A list of lecture topics from 2012 can be found here.