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Unformatted text preview: NAME → ISyE 3770 — Test 2 b Solutions — Fall 2008 This test is 85 minutes long. You are allowed two cheat sheets. Do not look at or start the test until you are told to do so. When we ask you to return the test, stop immediately, hand the test in, and do not utter a word to anyone. Do not communicate via mind power with anyone. Do not show any work other than your answers on this sheet. Good luck! Put your nice, simple answers here... 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 1 1. Suppose X has p.d.f. f ( x ) = 3 x 2 , < x < 1 . Find P (0 ≤ X ≤ 1 / 4  ≤ X ≤ 1 / 2) . Solution : P (0 ≤ X ≤ 1 / 4  ≤ X ≤ 1 / 2) = P (0 ≤ X ≤ 1 / 4 ∩ ≤ X ≤ 1 / 2) P (0 ≤ X ≤ 1 / 2) = P (0 ≤ X ≤ 1 / 4) P (0 ≤ X ≤ 1 / 2) = R 1 / 4 3 x 2 dx R 1 / 2 3 x 2 dx = x 3  1 / 4 x 3  1 / 2 = 1 / 8 / 2. If f ( x ) = x/ 2 , < x < 2 , find E [ X ] . Solution: E [ X ] = Z R xf ( x ) dx = Z 2 x · x 2 dx = x 3 6 fl fl fl fl 2 = 4 3 / 3. If f ( x ) = x/ 2 , < x < 2 , find E [1 /X ] . Solution : E • 1 X ‚ = Z R 1 x f ( x ) dx = Z 2 1 x · x 2 dx = 1 / 4. If E [ X ] = 2 and E [ X 2 ] = 10 , find Var (2 X 1) . Solution : Var (2 X 1) = 4 Var ( X ) = 4( E [ X 2 ] E [ X ] 2 ) = 4(10 4) = 24 / 5. True or False? If E [ X ] = μ , then E £ ( X μ ) 2 / = E [ X 2 ] μ 2 for any random variable X ....
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This note was uploaded on 08/27/2011 for the course ISYE 3770 taught by Professor Goldsman during the Spring '07 term at Georgia Tech.
 Spring '07
 goldsman

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