EECS 422: Random Processes in Communications and Control I

Winter 2010

Lecture 1 | Introduction, Probability spaces. |

Lecture 2 | Properties of probability measures, conditional probabilities, independence. |

Lecture 3 | Independent trials, combinations, permutations. |

Lecture 4 | Random variables, distributions, discrete Random variables, p.m.f.'s |

Lecture 5 | Continuous random variables, densities, mixed random variables, examples of common distributions. |

Lecture 6 | Gaussian random variables, conditional distributions, functions of random variables. |

Lecture 7 | Expected values, moments. |

Lecture 8 | Markov inequality, Chebyshev's inequality, Chernoff bounds, moment generating functions, Characteristic functions. |

Lecture 9 | Introduction to random vectors, joint distributions, joint densities, marginals. |

Lecture 10 | More on Random vectors: independence, moments, correlation. |

Lecture 11 | Two jointly Gaussian random variables, functions of random vectors. |

Lecture 12 | Linear transformations of random vectors, condition distributions. |

Lecture 13 | More on conditional distributions, conditional expectation, MMSE estimation. |

Lecture 14 | More on MMSE estimation; scalar Gaussian case. |

Lecture 15 | MMSE estimation - vector case; jointly Gaussian Random variables (N>2). |

Lecture 16 | More on Jointly Gaussian random variables and MMSE estimation; covariance matrices. |

Lecture 17 | Laws of large numbers, mean-square convergence, convergence in probability. |

Lecture 18 | Almost sure convergence; strong law of large numbers; convergence in distribution; the central limit theorem. |

Lecture 19 | More on the central limit theorem; random processes. |

Lecture 20 | Discrete-time Random processes: Bernoulli processes, Binomial counting process, simple random walk; stationarity, Memoryless and Markov properties, independent and stationary increments. |

Lecture 21 | Random walk on a graph; Poisson processes. |

Lecture 22 | More on Poisson processes; random telegraph signals. |

Lecture 23 | Formally specifying random processes, Kolmorogorov's consistency conditions; mean and correlation/covariance functions; wide sense stationarity. |

Lecture 24 | Properties of covariance functions; Brownian motion. |

Lecture 25 | Mean-squared continuity, mean-squared derivatives. |

Lecture 26 | Mean-squared integration; random processes and linear systems. |

Lecture 27 | Spectral analysis for random processes; application to linear systems. |

Lecture 28 | Introduction to optimal filtering; overview of related courses. |