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TEXT_solutions

# TEXT_solutions - Probability and Stochastic Processes A...

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Probability and Stochastic Processes A Friendly Introduction for Electrical and Computer Engineers SECOND EDITION Problem Solutions May 2004 Draft Roy D. Yates and David J. Goodman May 22, 2004 This solution manual remains under construction. The current count is that 575 out of 695 problems in the text are solved here, including all problems through Chapter 5. At the moment, we have not confirmed the correctness of every single solution. If you find errors or have suggestions or comments, please send email to [email protected] . M ATLAB functions written as solutions to homework probalems can be found in the archive matsoln.zip (available to instructors) or in the directory matsoln . Other M ATLAB func- tions used in the text or in these hoemwork solutions can be found in the archive matcode.zip or directory matcode . The .m files in matcode are available for download from the Wiley website. Two oter documents of interest are also available for download: A manual probmatlab.pdf describing the matcode.m functions is also available. The quiz solutions manual quizsol.pdf . A web-based solution set constructor for the second edition is also under construction. A major update of this solution manual will occur prior to September, 2004. 1

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Problem Solutions – Chapter 1 Problem 1.1.1 Solution Based on the Venn diagram M O T the answers are fairly straightforward: (a) Since T M = φ , T and M are not mutually exclusive. (b) Every pizza is either Regular ( R ), or Tuscan ( T ). Hence R T = S so that R and T are collectively exhaustive. Thus its also (trivially) true that R T M = S . That is, R , T and M are also collectively exhaustive. (c) From the Venn diagram, T and O are mutually exclusive. In words, this means that Tuscan pizzas never have onions or pizzas with onions are never Tuscan. As an aside, “Tuscan” is a fake pizza designation; one shouldn’t conclude that people from Tuscany actually dislike onions. (d) From the Venn diagram, M T and O are mutually exclusive. Thus Gerlanda’s doesn’t make Tuscan pizza with mushrooms and onions. (e) Yes. In terms of the Venn diagram, these pizzas are in the set ( T M O ) c . Problem 1.1.2 Solution Based on the Venn diagram, M O T the complete Gerlandas pizza menu is Regular without toppings Regular with mushrooms Regular with onions Regular with mushrooms and onions Tuscan without toppings Tuscan with mushrooms 2
Problem 1.2.1 Solution (a) An outcome specifies whether the fax is high ( h ) , medium ( m ) , or low ( l ) speed, and whether the fax has two ( t ) pages or four ( f ) pages. The sample space is S = { ht , h f , mt , m f , lt , l f } . (1) (b) The event that the fax is medium speed is A 1 = { mt , m f } . (c) The event that a fax has two pages is A 2 = { ht , mt , lt } . (d) The event that a fax is either high speed or low speed is A 3 = { ht , h f , lt , l f } .

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