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# QZ 4-D - X f X x f X x = âˆ 1 6 x dy x = âˆ 1 6 x dy x = 1...

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STAT 400 Fall 2011 Version D 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 ) = 6 x , 0 < x < y < 1, zero otherwise. a) (4) Find the probability P ( X + Y < 1 ) . P ( X + Y > 1 ) = - 2 1 0 1 6 dx dy x x x = ( ) - 2 1 0 2 1 6 dx x x = ( ) - 2 1 0 2 12 6 dx x x = ( ) 0 2 1 4 3 3 2 x x - = 8 4 4 3 - = 4 1 . b) (3) Find the marginal probability density function of X, f X (

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Unformatted text preview: X, f X ( x ). f X ( x ) = âˆ« 1 6 x dy x = âˆ« 1 6 x dy x = ( ) 1 6 x x-, 0 < x < 1. 1. (continued) f ( x , y ) = 6 x , 0 < x < y < 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 Y ( y ) = âˆ« y dx x 6 = 3 y 2 , 0 < y < 1. f ( x , y ) â‰  f X ( x ) â‹… f Y ( y ). â‡’ X and Y are NOT independent ....
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