# IE523_Hw4 - IE 523 Probabilistic Analysis Homework 4 Due...

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1 IE 523 Probabilistic Analysis Homework # 4 Due: Friday, November 13, 17:00. To be submitted to EA 323. Question 1: The transforms associated with two independent discrete random variables X and Y are () 7 81 24 11 , 22 s e ss XY Ms e e Ms e ⎛⎞ =+ = ⎜⎟ ⎝⎠ . Find () ( ) [ ] 2 15 , 5 , , p pE X E Y ⎡⎤ ⎣⎦ , and 15 PX Y += . Question 2: Suppose that ( ) 63 21 3 X s = −− . Find the PDF of the associated random variable. Question 3: Let Y be exponentially distributed with parameter 1, and let Z be uniformly distributed over the interval [0, 1]. Use convolution to find the PDF of YZ . Question 4: The transform associated with N , the total number of living groups contacted about a blood drive, is 10 12 33 s N e . a. Determine the PMF of N . b. Let the number K of people in any particular living group, be an independent random variable with associated transform 4 1 5 4 1 5 s K s e e = Find () [ ] , K p kEK , and var K . c. Let L be the total number of people whose living groups are contacted about the blood drive.

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## This note was uploaded on 04/15/2010 for the course INDUSTRIAL ie513 taught by Professor Zeynephuygur during the Spring '10 term at Bilkent University.

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IE523_Hw4 - IE 523 Probabilistic Analysis Homework 4 Due...

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