HW1_soln

HW1_soln - Probability and Stochastic Processes A Friendly...

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Unformatted text preview: Probability and Stochastic Processes: 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 1.3.2 1.3.5 1.4.2 1.4.4 1.5.3 1.5.4 and 1.5.5 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, 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 (e) The event that more than one circuit is acceptable is C = { aaa, aaf, afa, faa } . (4) The event that at least two circuits fail is D = { ffa, faf, aff, fff } . (5) (f) Inspection shows that C ∩...
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This note was uploaded on 02/11/2012 for the course EEE 352 taught by Professor Ferry during the Spring '08 term at ASU.

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HW1_soln - Probability and Stochastic Processes A Friendly...

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