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hw4 - UCSD ECE153 Prof Young-Han Kim Handout#15 Thursday...

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UCSD ECE153 Handout #15 Prof. Young-Han Kim Thursday, April 21, 2011 Homework Set #4 Due: Thursday, April 28, 2010 1. Two independent uniform random variables. Let X and Y be independently and uni- formly drawn from the interval [0 , 1]. (a) Find the pdf of U = max( X, Y ) . (b) Find the pdf of V = min( X, Y ). (c) Find the pdf of W = U - V . (d) Find the probability P {| X - Y | ≥ 1 / 2 } . 2. Waiting time at the bank. 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 find that both tellers are busy but that nobody else is waiting to be served. You are served by the first available teller once he/she becomes free. Let the random variable Y denote your waiting time. Find the pdf of Y . 3. Two envelopes. An amount A is placed in one envelope and the amount 2 A is placed in another envelope. The amount A is fixed but unknown to you. The envelopes are shuffled and you are given one of the envelopes at random. Let X denote the amount you observe in this envelope. Designate by Y the amount in the other envelope. Thus ( X, Y ) = braceleftBigg ( A, 2 A ) , with probability 1 2 , (2 A, A ) , with probability 1 2 .
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