final03

final03 - EEE350: Final Exam Spring 2003 Examination Date:...

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EEE350: Final Exam Spring 2003 Examination Date: May 14th Examination Time: 7:40–9:30am Student Name: Student ID: 1. This exam consists of six problems (Problem 6 is a bonus problem). You need to provide the necessary details in order to get credits. 2. Three-page crib sheets are allowed. 3. The standard Gaussian CDF is provided.
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1. (20’) Suppose X and Y are independent Gaussian random variables, with X N (0 , 1) and Y N (1 , 4). (a) (4’) Find the probability P ( X 2 4). (b) (8’) Let W = X - 2 Y . Find the probability P ( - 2 - 3 W ≤ - 2 + 3). 1
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(c) (8’) Define Z = X 2 , and find the probability density function (PDF) of Z . 2. (20 points) In a communication system, information bits are transmitted from source to destination. However, due to the ambient white Gaussian noise in the communication channel, an information bit may be received erroneously by the time it arrives at the destination. Assume that the information bits are transmitted independently, and let
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final03 - EEE350: Final Exam Spring 2003 Examination Date:...

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