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problemset23

problemset23 - b Find the density f X x of X c Find the...

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STAT/MA 416 October 21, 2011 Problem Set 23 Name: 1. Consider a pair of random variables X,Y with constant joint density on the triangle with vertices at (0 , 0), (3 , 0), and (0 , 3). a. Are X and Y independent? Why or why not? b. Find the density f X ( x ) of X . c. Find the density f Y ( y ) of Y . 1

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2. Consider a pair of random variables X,Y with constant joint density on the quadrilateral with vertices (0 , 0), (2 , 0), (2 , 6), (0 , 12). a. Are X and Y independent? Why or why not? b. Find the density f X ( x ) of X . c. Find the density f Y ( y ) of Y . 2
3. Let X,Y have joint density f X,Y ( x,y ) = 14 e - 2 x - 7 y for x > 0 and y > 0; and f X,Y ( x,y ) = 0 otherwise. a. Are X and Y independent? Why or why not? b. Find the density f X ( x ) of X . c. Find the density f Y ( y ) of Y . 3

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4. Suppose X,Y has joint density f X,Y ( x,y ) = ( 1 / 16 if - 2 x 2 and - 2 y 2, 0 otherwise. a. Are X and Y independent? Why or why not?

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Unformatted text preview: b. Find the density f X ( x ) of X . c. Find the density f Y ( y ) of Y . 4 5. Suppose X,Y has joint density f X,Y ( x,y ) = ( 1 9 (3-x )(2-y ) if 0 ≤ x ≤ 3 and 0 ≤ y ≤ 2, otherwise. a. Are X and Y independent? Why or why not? b. Find the density f X ( x ) of X . c. Find the density f Y ( y ) of Y . 5 6. Design your own problem and solution. Create your own problem about a pair of jointly-distributed continuous random variables X and Y that may or may not be indepen-dent. State whether they are independent or dependent, and then calculate their densities f X ( x ) and f Y ( y ). 6...
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problemset23 - b Find the density f X x of X c Find the...

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