oldmidterm2

oldmidterm2 - UCSD ECE153 Prof. Young-Han Kim Handout #20...

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UCSD ECE153 Handout #20 Prof. Young-Han Kim Tuesday, May 3, 2011 Midterm Examination (Spring 2008) (Total: 80 points) 1. First available teller (20 points). Consider a bank with two tellers. The service times for the tellers are independent exponentially distributed random variables X 1 Exp( λ 1 ) and X 2 Exp( λ 2 ), respectively. You arrive at the bank and Fnd that both tellers are busy but that nobody else is waiting to be served. You are served by the Frst available teller once he/she becomes free. Let the random variable Y denote your waiting time. ±ind the pdf of Y . Note: The pdf of an Exp( λ ) random variable X is f X ( x ) = b λe - λx , x 0 , 0 , otherwise. 2. Sum of packet arrivals (40 points). Consider a network router with two types of incoming packets, wireline and wireless. Let the random variable N 1 ( t ) denote the number of wireline packets arriving during time (0 , t ] and let the random variable N 2 ( t ) denote the number of wireless packets arriving during time (0
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oldmidterm2 - UCSD ECE153 Prof. Young-Han Kim Handout #20...

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