310C: HOMEWORK SETS 2010363310c: Homework Sets 2010Homework rules:Arguments should be precise, concise and correct. We expectrigorous and complete proofs. Answers should be clean and legible. Please use aseparate sheet of paper for each problem (easier for you to work with, and easier tograde), andstaple together all the sheets you hand in.Submit solutions only for 32of the 40 assigned exercises (only the first 32 exercises you submit will be graded).When solving one exercise you may cite any other exercise, without proving it.Problems can be solved in a group effort, but students shouldindependentlywritetheir own solutions!Homework 1: due April 6th.Review the setting and construction of Kolmogorov’s extension theorem (in Sec-tion 1.4.2), as well as Definition 3.4.8 of the Poisson process and the definitionand main properties of Gaussian random vectors (from Section 3.5).Then, readeverything in Sections 7.1–7.2 that was not covered in lectures by Apr. 2nd.
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Markov chain, Andrey Markov, Random walk, homework sets