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HW1-solution

# HW1-solution - Probability and Stochastic Processes A...

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A Friendly Introduction for Electrical and Computer Engineers Edition 2 Roy D. Yates and David J. Goodman Problem Solutions : Yates and Goodman, 1.2.1 1.2.2 1.2.4 1.3.1 1.3.2 1.3.4 1.4.1 1.4.4 1.5.2 and 1.5.3 Problem 1.2.1 Solution (a) An outcome specifes 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, hf, mt, mf, lt, lf } . (1) (b) The event that the Fax is medium speed is A 1 = { mt, mf } . (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, hf, lt, lf } . (e) Since A 1 A 2 = { mt } and is not empty, A 1 , A 2 , and A 3 are not mutually exclusive. (F) Since A 1 A 2 A 3 = { ht, hf, mt, mf, lt, lf } = S, (2) the collection A 1 , A 2 , A 3 is collectively exhaustive. Problem 1.2.2 Solution (a) The sample space oF the experiment is S = { aaa, aaf, afa, faa, ffa, faf, aff, fff } . (1) (b) The event that the circuit From Z Fails is Z F = { aaf, aff, faf, fff } . (2) The event that the circuit From X is acceptable is X A = { aaa, aaf, afa, aff } . (3) (c) Since Z F X A = { aaf, aff } 6 = φ , Z F and X A are not mutually exclusive. (d) Since Z F X A = { aaa, aaf, afa, aff, faf, fff } 6 = S , Z F and X A are not collectively exhaustive. 1

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HW1-solution - Probability and Stochastic Processes A...

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