EECS 422: Random Processes in Communications and Control I

Winter 2018

Reading | ||

Lecture 1 | Introduction, Probability spaces, Sigma Algebras, Properties of probability measures, | Sect. 1.1-1.2 |

Lecture 2 | Conditional probability, Statistical independence, conditional independence, Repeated trials, random variables, CDFs, PMFs, PDFs, mixed and singular random variables. | Sect. 1.3.1-1.3.3 |

Lecture 3 | Multiple random variables, joint distributions, stochastic processes, the Bernoulli process. | Sect. 1.3.4 -1.4 |

Lecture 4 | Expected values, moments, sums of random variables, conditional expectation, The coupon collector problem. | Sect. 1.5 |

Lecture 5 | Markov's inequality, Chebyshev's inequality, Chernov Bounds. | Sect. 1.6 |

Lecture 6 | Moment generating functions and sums of independent random variables, log-moment generating functions, Convergence of random variables: mean-squared convergence, convergence in probability, the weak law of large numbers. | Sect. 1.6-1.7 |

Lecture 7 | Almost sure convergence, the strong law of large numbers, convergence in distribution,, the central limit theorem. | Sect. 1.7 & 5.2 |

Lecture 8 | Central limit theorem examples, Characteristic functions, Counting Processes and the Poisson Process, memoryless property, fresh-restart property. | Sect. 2.1-2.2 |

Lecture 9 | More on Poisson Processes: increment properties, alternative definitions, Splitting and combining Poisson Processes. | Sect. 2.2-2.3 |

Lecture 10 | Markov Chains: definitions, transition Matrices/Graphs, first-step analysis. | Notes |

Lecture 11 | MID-TERM EXAM | |

Lecture 12 | Markov Chains: Stationary distributions, state classifications, recurrence, periodicity. | Sect. 4.1-4.2 & 6.2 |

Lecture 13 | Markov Chains: ergodic chains, convergence to stationary distributions, balance equations. | Sect. 4.2-4.3, 6.1-6.2 |

Lecture 14 | Gaussian random vectors: linear transformations, moment generating functions. | Sect. 3.1 -3.3 |

Lecture 15 | Gaussian random vectors: joint probability distributions and properties of covariance matrices | Sect. 3.3 -3.4 |

Lecture 16 | Conditioning and Gaussian random vectors; Introduction to estimation | Sect. 3.5, Sect. 10.1. |

Lecture 17 | Estimation and Gaussian random vectors, linear estimation, Intro. to Gaussian Processes. | Sect. 10.2-10.3. |

Lecture 18 | Stationary processes, Properties of covariance functions, Wiener processes. | Sect. 3.6.1, 3.6.9 |

Lecture 19 | More on Wiener prcess, random processes and linear systems, spectral density. |

A list of lecture topics from 2017 can be found here.