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problemset26 - Y 4 5 Suppose X,Y has joint density f X,Y...

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STAT/MA 416 October 28, 2011 Problem Set 26 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. Find the expected value of the sum of X and Y , i.e., find E ( X + Y ). b. Find the variance of X , i.e., find Var( X ). 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 variance of X , i.e., find Var X . b. Find the variance of Y , i.e., find Var Y . 2
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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. Find the variance of the sum of X and Y , i.e., find Var( X + 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.
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Unformatted text preview: 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. Find the expected value of X 2 + Y 3 , i.e., find E ( X 2 + Y 3 ). 5 6. Design your own problem and solution. Create your own problem about the expected value of a function of a continuous random variable, or about the variance 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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