Homework6 - normal random variables Define Y 1 = 2 X 1 X 2...

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ST561 Fall 2010 Homework 6 Due: Monday, Nov. 8th, 2010 1. Consider any two random variables X 1 and X 2 with V ( X 1 ) = V ( X 2 ) < . Let Y 1 = X 1 + X 2 and Y 2 = X 1 - X 2 . (a) Show that Cov ( Y 1 , Y 2 ) = 0. (b) Use the result in (a) to construct a pair of random variables which are uncorrelated and independent. (c) Use the result in (a) to construct a pair of random variables which are uncorrelated but dependent. 2. Let X 1 and X 2 are independent standard
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Unformatted text preview: normal random variables. Define Y 1 = 2 X 1 + X 2 and Y 2 = X 1-X 2 . (a) What is the joint distribution of ( Y 1 ,Y 2 )? (b) What are the marginal distributions of Y 1 and Y 2 ? (c) What is the conditional distribution of Y 1 given Y 2 = y 2 ? 3. Textbook Page 170, 3.6.3. 4. Textbook Page 170, 3.6.5. 5. Textbook Page 170, 3.6.7. 1...
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