# QZ 4-C - f Y y f Y y = âˆ 1 3 y dx x = y x 1 2 3 2 = 2 1 3...

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STAT 400 Fall 2011 Version C Name ANSWERS . Quiz 4 (10 points) Be sure to show all your work; your partial credit might depend on it. If the answer is a function, its support must be included. No credit will be given without supporting work. 1. Let the joint probability density function for ( X , Y ) be f ( x , y ) = 3 x , 0 < y < x < 1, zero otherwise. a) (4) Find the probability P ( X + Y > 1 ). P ( X + Y > 1 ) = - 1 2 1 1 3 dx dy x x x = ( ) - 1 2 1 1 2 3 dx x x = ( ) - 1 2 1 2 3 6 dx x x = 2 1 1 2 3 2 2 3 - x x = 8 3 8 2 2 3 2 + - - = 8 5 . b) (3) Find the marginal probability density function of Y,

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Unformatted text preview: f Y ( y ). f Y ( y ) = âˆ« 1 3 y dx x = y x 1 2 3 2 = ( ) 2 1 3 2 y-, 0 < y < 1. 1. (continued) f ( x , y ) = 3 x , 0 < y < x < 1, zero otherwise. c) (3) Are X and Y independent? Justify your answer. No credit will be given without proper justification. Circle one: Yes. No. The support of ( X, Y ) is not a rectangle. â‡’ X and Y are NOT independent . OR f X ( x ) = âˆ« x dy x 3 = 3 x 2 , 0 < x < 1. f ( x , y ) â‰  f X ( x ) â‹… f Y ( y ). â‡’ X and Y are NOT independent ....
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## This note was uploaded on 02/15/2012 for the course STAT 400 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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QZ 4-C - f Y y f Y y = âˆ 1 3 y dx x = y x 1 2 3 2 = 2 1 3...

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