20061ee131A_1_131a3

# 20061ee131A_1_131a3 - EE 131A Homework#3 Winter 2006 Due...

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Unformatted text preview: EE 131A Homework #3 Winter 2006 Due February 9th K. Yao Read Leon-Garcia, pp. 84–119 1. There are three power plants (denoted by i = 1 , 2 , 3) which can be either working or not working. If plant i is working, we denote it by a i = 1 and if it is not working, we denote it by a i = 0 . Then denote the status of the plants by the eight vectors of the form ( a 1 ,a 2 ,a 3 ) , where each a i can be either 1 or 0 . The probability of the eight events are given by: P[(0,0,0)]=.07; P[(0,0,1)]=.04; P[(0,1,0)]=.03; P[(0,1,1)]=.18;P[(1,0,0)]=.16; P[(1,0,1)]=.18; P[(1,1,0)]=.21; P[(1,1,1)]=.13. Denote the r.v. X as the total number of plants working. That is define X = a 1 + a 2 + a 3 . a. Draw a sample space S with these eight labeled elementary events. For the defined r.v. X, draw a line from each of the eight events to the real-line (say drawn hori- zontally) with the value on the real-line indicating the mapping of X (( a 1 ,a 2 ,a 3 )) ....
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20061ee131A_1_131a3 - EE 131A Homework#3 Winter 2006 Due...

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