statsquiz4

# statsquiz4 - Quiz 4 Probability and Statistics Bernardo...

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Unformatted text preview: Quiz 4 Probability and Statistics Bernardo Guimaraes September 2009 1. Which of the following are probability density functions of 2 independent variables? (a) f X;Y ( x; y ) = 2 ; &amp; x &amp; y &amp; 1 , otherwise f X;Y ( x;y ) = 0 . (b) f X;Y ( x;y ) = 2 ; &amp; x &amp; 1 ; &amp; y &amp; 1 , otherwise f X;Y ( x; y ) = 0 . (c) f X;Y ( x;y ) = xy; &amp; x &amp; 1 ; &amp; y &amp; 1 , otherwise f X;Y ( x; y ) = 0 . (d) f X;Y ( x;y ) = 4 xy; &amp; x &amp; 1 ; &amp; y &amp; 1 , otherwise f X;Y ( x; y ) = 0 . (e) f X;Y ( x;y ) = x + y; &amp; x &amp; 1 ; &amp; y &amp; 1 , otherwise f X;Y ( x;y ) = 0 . 2. Let X and Y be independent random variables such that E ( X ) = 1 , E ( Y ) = 1 , &amp; 2 X = 1 and &amp; 2 Y = 2 . Then E ( XY ) is: (a) 1 (b) 2 (c) 3 (d) 4 (e) there is not enough information to calculate E ( XY ) . (For 3 and 4) Let X and Y be continuous random variables such that f X;Y ( x; y ) = 2 ; &amp; y &amp; x &amp; 1 (otherwise f X;Y ( x; y ) = 0 ). 3. The marginal distribution of probability of Y is: (a) f Y ( y ) = 2 ; &amp; y &amp; 1 , otherwise f Y ( y ) = 0 ....
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## This note was uploaded on 02/28/2010 for the course ECO 211 taught by Professor Gilo during the Spring '10 term at Young Harris.

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statsquiz4 - Quiz 4 Probability and Statistics Bernardo...

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