310C: HOMEWORK SETS 2010 363 310c: Homework Sets 2010 Homework rules: Arguments should be precise, concise and correct. We expect rigorous and complete proofs. Answers should be clean and legible. Please use a separate sheet of paper for each problem (easier for you to work with, and easier to grade), and staple together all the sheets you hand in. Submit solutions only for 32 of the 40 assigned exercises (only the Frst 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 e±ort, but students should independently write their 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 DeFnition 3.4.8 of the Poisson process and the deFnition and main properties of Gaussian random vectors (from Section 3.5). Then, read everything in Sections 7.1–7.2 that was not covered in lectures by Apr. 2nd. Exercises 7.1.12*, 7.1.13, 7.2.3, 7.2.7, 7.2.9* and 7.2.13.
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