EECS 422: Random Processes in Communications and Control I

Winter 2016

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

Lecture 2 | Repeated trials, random variables, CDFs, PMFs, PDFs, mixed and singular random variables, Multiple random variables, joint distributions, stochastic processes. |

Lecture 3 | The Bernoulli process, expected values, moments, sums of random variables, conditional expectation. |

Lecture 4 | The coupon collector problem, Markov's inequality, Chebyshev's inequality, Chernov Bounds, moment generating functions. |

Lecture 5 | Chernov bound examples, Moment generating funcitons and sums of independent random variables, log-moment generating functions. |

Lecture 6 | Convergence of random variables: mean-squared convergence, convergence in probability, almost sure convergence, laws of large numbers. |

Lecture 7 | The strong law of large numbers, convergence in distribution, characteristic functions, the central limit theorem. |

Lecture 8 | Counting Processes and the Poisson Process. |

Lecture 9 | Splitting and combining Poisson Processes, Markov Property, Markov Chains: transistion matrices/graphs. |

Lecture 10 | Markov Chains: first-step analysis, state classifications, stationary distributions. |

Lecture 11 | Markov Chains: Stationary distributions, Balance equations; Introduction to Gaussian Random Vectors. |

MID-TERM EXAM | |

Lecture 12 | More on Gaussian random vectors. |

Lecture 13 | Conditioning and Gaussian random vectors; introduction to Gaussian Processes. |

Lecture 14 | Stationary processes, Properties of covariance functions, Weiner processes. |

Lecture 15 | Orthonormal expansions, Gaussian sinc processes, filtered Gaussian sinc processes. |

Lecture 16 | Second-order characterizations of filtered random processes, Spectral densities; introduction to estimation. |

Lecture 17 | MMSE estimation, estimation and Gaussian random vectors, LLSE estimation, optimal filtering. |

A list of lecture topics from 2015 can be found here.