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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 pmfs of X and Y ? 1 OR 3500/5500, Summer09, 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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 Summer '08
 WEBER

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