# HW 1 - EC489.02 Summer 2011 Homework 1 The due date for...

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EC489.02 Summer 2011 Homework 1 The due date for this assignment is Wednesday July 6, 12:00 . 1. Show that Z 1 1 Z 1 0 Z 1 x 2 0 6 e x 1 e 2 x 2 e 3 x 3 dx 1 dx 2 dx 3 = 1 2 e 1 + e 2 ± e 3 : 2. This Exercise is related to the Proof of Theorem 4 : 14 : In particular, you will be asked to prove an equality in part (c), which was used to prove the second part of Theorem 4 : 14 : (a) If X 1 and X 2 are random variables, where 1 = E [ X 1 ] and 2 = E [ X 2 ] ; and a 1 and a 2 are constants, then show that E ² [ a 1 ( X 1 1 ) + a 2 ( X 2 2 )] 2 ³ = a 2 1 E ´ ( X 1 1 ) 2 µ +2 a 1 a 2 E [( X 1 1 )( X 2 2 )] + a 2 2 E ´ ( X 2 2 ) 2 µ : (b) For i = 1 ; 2 and j = 1 ; 2 ; show that 2 XX i<j a i a j E ´ ( X i i )( X j j ) µ = 2 a 1 a 2 E [( X 1 1 )( X 2 2 )] ; where the double summation PP i<j extends over all values of i and j , from 1 to 2 , for which i < j: (c) Now, we move on to the case where i = 1 ; :::; n and j = 1 ; :::; n:

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## This note was uploaded on 10/25/2011 for the course ECON 501 taught by Professor Zobuz during the Spring '11 term at Istanbul Technical University.

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HW 1 - EC489.02 Summer 2011 Homework 1 The due date for...

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