# hw1 - ORIE 4580/5580/5581 Homework Assignment 1 Due by Sep....

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ORIE 4580/5580/5581 Homework Assignment 1 Due by Sep. 14, 11:00 am, in the drop-box located on the second ﬂoor of Rhodes Hall. Please note that this homework deviates from our announced schedule in the syllabus and it is due on a Wednesday. 1. The probability density function of the random variable X is given by f X ( x ) = { 3 28 x 2 3 14 x + 3 28 if 2 x 2 0 otherwise . Let the random variable Y be deﬁned as Y = X 2 . a) Find the cumulative distribution function of the random variable Y . (Hint: P { X 2 y } = P { ? X ? } .) b) Find the probability density function of the random variable Y . c) Compute E { Y } and V ar ( Y ). 2. The probability density function of the random variable X is given by f X ( x ) = { a x + 1 8 if 0 x 4 0 otherwise . a) Compute the value of a . b) Let the random variable Y be deﬁned as Y = X , where ⌊·⌋ is the “round down” operator (that is, for example, 2 . 5 = 2 , ⌊− 2 . 5 = 3 , ⌊− 3 = 3). Find the probability mass function of

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## This note was uploaded on 03/08/2012 for the course ORIE 4580 at Cornell.

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hw1 - ORIE 4580/5580/5581 Homework Assignment 1 Due by Sep....

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