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Unformatted text preview: ( x , 2 x ). 6. Suppose X N (0 , 1), and dene Y = X 2 . Are X and Y uncorrelelated? Are X and Y independent? Find the p.d.f. of Y . Are X and Y jointly continuous? 7. Show that cov( aX + b, cY + d ) = ac cov( X, Y ). 1 8. Suppose X N (0 , 2 ). Use the ch.f. of X to Fnd an expression for E [ X n ], n Z + . Problems from the Grimmett & Stirzaker text: 1. Ex 1.4.4 2. Ex 1.4.5. Hint: Let C i be the event that the i th door conceals the car, let G be the event that you see a goat, and let B be the event that you see Bill. 3. Ex 1.5.1. 4. Ex 1.5.2 5. Ex 1.5.7. 6. Prob. 1.8.5 7. Prob. 1.8.6. 8. Prob. 1.8.19. 9. Prob. 1.8.20. 10. Prob. 1.8.30. 2...
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- Spring '08