problemset25

# problemset25 - E X b Find the expected value E Y 4 5...

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STAT/MA 416 October 26, 2011 Problem Set 25 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). Find the expected value E ( X ). (Notice that, by symmetry, E ( Y ) is just the same!) 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. Find the expected value E ( X ). b. Find the expected value E ( 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. Find the expected value E ( X ). b. Find the expected value E ( Y ). 3

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4. Let X,Y have joint density f X,Y ( x,y ) = 18 e - 2 x - 7 y for 0 < y < x ; and f X,Y ( x,y ) = 0 otherwise. a. Find the expected value

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Unformatted text preview: E ( X ). b. Find the expected value E ( 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. Find the expected value E ( X ). b. Find the expected value E ( Y ). 5 6. Design your own problem and solution. Create your own problem about the expected value of a continuous random variable. Design your problem in such a way that you would ﬁnd it enjoyable and also interesting (i.e., not completely trivial) if you found this problem in a probability book. Please provide the answer for your problem too. 6...
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problemset25 - E X b Find the expected value E Y 4 5...

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