ee464_hw5

# ee464_hw5 - EE 464, Mitra Homework 5 Due Friday, February...

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EE 464, Mitra Spring 2009 Homework 5 Due Friday, February 20, 2009, 9AM 464 Box This problem set investigates properties of the expectation operator, and requires the calculation of moments of random variables and functions of random variables. 1. Show the following properties: (a) Show that | E [ X ] | ≤ E [ | X | ] (hint: use the triangle inequality) (b) Let X and Y be two non-negative random variables. Show that if F X ( x ) F Y ( x ) then E [ X ] E [ Y ] . Find a counterexample for the inverse statement. That is show that if E [ X ] E [ Y ] then this does not imply F X ( x ) F Y ( x ) . (c) Let X be a random variable and c R , a constant. Then show: Var [ c ] = 0 , Var [ X + c ] = Var [ X ] , Var [ cX ] = c 2 Var [ X ] . These properties have been provided in lecture, I now want you to show them explicitly. 2. Let X be a uniform random variable, U [0 , 2] . Compute the pdf of Y = g ( X ) where g ( x ) is deﬁned below. 0 1

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## This note was uploaded on 02/02/2010 for the course EE 464 taught by Professor Caire during the Spring '06 term at USC.

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ee464_hw5 - EE 464, Mitra Homework 5 Due Friday, February...

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