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EE302%20hw1_fa06

# EE302%20hw1_fa06 - EE302 Homework#1 Assigned Due(by 4:30 in...

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{ } { } { } { } EE302 Homework #1 S S , , , , , , A , , , B , , , C , , , . / . A B C A B A C A C B A, B, C A, B C C, = 1 3 5 7 9 11 = 1 3 5 = 7 9 11 = 1 3 9 11 1 6 Pr ( ) Pr ( ) Pr ( ) Pr ( ) Pr ( ) Pr[( ) ] Assigned 8/29/06, Due 9/7/06 (by 4:30 in dropbox in MSEE 330) 1. A space is de ned as and three subsets as Assume that each element has probability Find the following probabilities: (a) (b) (c) (d) (e) (f) 2. Two fair coins are ipped, and the ips are independent.. (a) List all of the outcomes. How many outcomes are there? (b) List all of the events. How many events are there? (c) Find the probability one of the ips is a head, and the probability that one of the ips is a tail. (d) Find the probability that one of the ips is a head and one of the ips is a tail. (e) Find the probability that one of the ips is a head given one of the ips is a tail (f) Are the events {one of the ips is a head} and {one of the ips is a tail} mutually exclusive? Are they independent? You must justify your answers. 3. Three intermittent switches are in a box. Switches and work 75%, 50% and 25% of the time, respectively. Different switches work independently.

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