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Introduction. Probability axioms and random variables | PDF/PMF and CDF | ![]() |
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Introduction. Probability axioms and random variables | PDF/PMF and CDF | ![]() |
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Function of random variables Definitions of convergence | Convergence in probability, convergence with probability 1, convergence in distribution | ![]() |
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Function of random variables Definitions of convergence | Convergence in probability, convergence with probability 1, convergence in distribution | ![]() |
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Useful inequalities and law of large numbers. Central limit theorem | Markov inequality, Chebyshev inequality, Chernoff bound | ![]() |
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Useful inequalities and law of large numbers. Central limit theorem | Markov inequality, Chebyshev inequality, Chernoff bound | ![]() |
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Bernoulli process and Poisson process | Definitions and properties of Bernoulli and Poisson processes | ![]() |
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Bernoulli process and Poisson process | Definitions and properties of Bernoulli and Poisson processes | ![]() |
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Discrete-time Markov chains and steady-state behavior | Definition, state transition probability, Markov property | ![]() |
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Mixing time and midterm review | Role of second largest eigenvalues and midterm review | ![]() |
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M/M/1 queues | Poisson arrival and exponential service, analysis of waiting times | ![]() |
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M/M/1 queues | Poisson arrival and exponential service, analysis of waiting times | ![]() |
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M/G/1 queues and Pollaczek- Khinchin formula | Definition of M/G/1 queue and derivation of Pollaczek-Khinchin formula | ![]() |
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M/G/1 queues and Pollaczek- Khinchin formula | Definition of M/G/1 queue and derivation of Pollaczek-Khinchin formula | ![]() |
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Estimation theory and Expectation- Maximization (EM) algorithm | Bayesian estimation, expectation maximization | ![]() |
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Estimation theory and Expectation- Maximization (EM) algorithm | Bayesian estimation, expectation maximization | ![]() |
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Hidden Markov models (HMM) | Modeling uncertain pheonomena using hidden Markov models | ![]() |
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Hidden Markov models (HMM) | Modeling uncertain pheonomena using hidden Markov models | ![]() |
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Counting processes and Renewal processes | Definition of counting and renewal processes, and analysis | ![]() |
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Counting processes and Renewal processes | Definition of counting and renewal processes, and analysis | ![]() |
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Randomized algorithms | Applications of probability and stochastic processes to randomized algorithms | ![]() |
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Randomized algorithms | Applications of probability and stochastic processes to randomized algorithms | ![]() |
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Randomized algorithms and course review | Applications of probability and stochastic processes to randomized algorithms | ![]() |
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Randomized algorithms and course review | Applications of probability and stochastic processes to randomized algorithms | ![]() |