EECS 422: Random Processes in Communications and Control I

Winter 2011

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, properties of density functions, Conditional Distributions, functions of random variables, expected values and moments. |

Lecture 4 | Gaussian Random Variables, Markov's Inequality, Chebyshev's Inequality, Chernoff Bounds, Moment Generating Functions.y |

Lecture 5 | Characteristic Functions; random vectors, joint cdfs, pdfs and pmfs, marginal distributions. |

Lecture 6 | Independence of random variables, Functions of multiple random variables, linear transformations of random vectors, Expectation and moments of random vectors, correlation and covariance. |

Lecture 7 | Linear estimation; Jointly Gaussian pairs of random variables and their properties. |

Lecture 8 | Conditional probability distributions, Conditional expectation, iterated expectations. |

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

Lecture 10 | Jointly Gaussian random vectors, Covariance matrices, MMSE estimation for random vectors. |

Lecture 11 | Mean-square convergence, convergence in probability, convergence almost surely, Weak and Strong Laws of Large numbers |

Lecture 12 | Convergence in distribution, the central limit theorem; introduction to stochastic processes. |

Lecture 13 | Finite dimensional distributions and Kolmogorov's theorem, Stationary processes, memoryless processes, stationary increments, independent increments, Markov property, counting processes, random walks. |

Lecture 14 | Markov chains, transition matrices/graphs, n-step transistions, first-step analysis, stationary distributions. |

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 2010 can be found here.