hw-sln-02

hw-sln-02 - S07 EEE 350 Random Signal Analysis Homework 2...

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Unformatted text preview: S07 EEE 350 Random Signal Analysis Homework 2 Solutions Feb. 1st, 2007 Problem Solutions : Yates and Goodman, 1.4.1 1.4.2 1.4.4 1.5.3 1.5.4 1.5.5 and 1.5.6 Problem 1.4.1 Solution From the table we look to add all the disjoint events that contain H to express the proba- bility that a caller makes no hand-offs as P [ H ] = P [ LH ] + P [ BH ] = 0 . 1 + 0 . 4 = 0 . 5 . (1) In a similar fashion we can express the probability that a call is brief by P [ B ] = P [ BH ] + P [ BH 1 ] + P [ BH 2 ] = 0 . 4 + 0 . 1 + 0 . 1 = 0 . 6 . (2) The probability that a call is long or makes at least two hand-offs is P [ L ∪ H 2 ] = P [ LH ] + P [ LH 1 ] + P [ LH 2 ] + P [ BH 2 ] (3) = 0 . 1 + 0 . 1 + 0 . 2 + 0 . 1 = 0 . 5 . (4) Problem 1.4.2 Solution (a) From the given probability distribution of billed minutes, M , the probability that a call is billed for more than 3 minutes is P [ L ] = 1- P [3 or fewer billed minutes] (1) = 1- P [ B 1 ]- P [ B 2 ]- P [ B 3 ] (2) = 1- α- α (1- α )- α (1- α ) 2 (3) = (1- α ) 3 = 0 . 57 . (4)...
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This note was uploaded on 09/26/2008 for the course EEE 350 taught by Professor Duman during the Spring '08 term at ASU.

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hw-sln-02 - S07 EEE 350 Random Signal Analysis Homework 2...

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