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Unformatted text preview: if x < x 2 if 0 ≤ x < 1 2 3 if 1 ≤ x < 2 11 12 if 2 ≤ x < 3 1 if x ≥ 3 . ( a ) Plot this cdf. ( b ) What is P ( X > 1 / 2)? ( c ) What is P (2 < X ≤ 4)? ( d ) What is P ( X < 3)? ( e ) What is P ( X = 1)? Problem 4 Let X and Y be discrete random variables with joint pmf p XY ( i,Ni ) = 1 N + 1 ,i ∈ { , 1 ,...,N } What are the marginal pmf’s of X and Y ? 1 OR 3500/5500, Summer’09, Chen The following problem is optional for 3500 students, mandatory for students enrolled in 5500 Problem 5 Let X be a number randomly chosen from [0 , 1]. Denote Y n = 1 n d nX e where d x e denotes the smallest integer k so that k ≥ x . (a) What is the distribution of Y n ? (b) What is the distribution of Z n := XY n ? (c) Compute lim n →∞ P ( Y n ≤ x ) for 0 ≤ x ≤ 1. 2...
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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.
 Summer '08
 WEBER

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