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exam_1_sg_m4320_f2010_v1_0 - e.g the first example on page...

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Exam 1 study guide: Math 4320 Fall 2010 1. Material: Chapters 1 and 2 (1) probability spaces, random variables (discrete random variables and random variables with pdfs) (2) major discrete distributions: Bernoulli, binomial, Poisson, hypergeometric (3) major continuous distributions: uniform, exponential, normal (4) expectation, variance, higher moments (define and compute) (5) joint distributions of random vectors, marginal distributions (6) conditional probability (7) conditional expectation (definition, properties, computations) (8) conditional distributions (discrete conditional distributions and conditional pdfs) (9) computing probabilities and means by conditioning (
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Unformatted text preview: e.g. the first example on page 59 of Taylor and Karlin) (10) random sums (11) martingales (a) definition (b) show that a given stochastic process is a martingale (c) maximal inequality (12) Markov inequality 2. Material: Chapter 3 (1) definition of a Markov chain (2) transition probability matrices (a) computations with a given transition probability matrix (b) find the transition probability matrix given a description of the model (3) classes of Markov chains (a) absorbing Markov chains (b) random walks (4) first-step analysis (Exam 1 will contain at least 1 problem that requires first-step analysis) 1...
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