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Unformatted text preview: Y = X 1 X 1 + X 2 , the proportion of time that the machine is in operation during any one operation-repair cycle. Problem 4 Let X and Y be independent random variables, X a standard uniform, and Y a standard exponential random variable. Find the density of the sum Z = X + Y . Caution : two dierent cases come up here. The following problem is optional for 3500 students, mandatory for students enrolled in 5500 Problem 5 If X 1 ,X 2 ,...,X n are independent Exp( ), show that for n 2, the density of Y := X 1 + ... + X n is given by f Y ( y ) = n ( n-1)! e-y y n-1 , y Hence, argue that Y follows Gamma( ,n ) using induction on n . 1...
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This note was uploaded on 09/22/2009 for the course ORIE 3500 taught by Professor Weber during the Summer '08 term at Cornell University (Engineering School).
- Summer '08