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Unformatted text preview: 1 NAME → ISyE 3770 — Test 2a Solutions — Fall 2009 This test is 55 minutes long. You are allowed one cheat sheet. Put your nice, simple answers here... 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15(a). 15(b). 15(c). 15(d). 15(e). 15(f). 15(g). 16. 17. 18. 19. 20. 2 1. Suppose X has p.d.f. f ( x ) = 2 x , 0 ≤ x ≤ 1. Find E [ 2 X 5]. Solution: E [ X ] = Z 1 2 x 2 dx = 2 3 ⇒ E [ 2 X 5] = 2 E [ X ] 5 = 19 3 ♦ 2. TRUE or FALSE? E [ X 2 ] ≤ ( E [ X ]) 2 . Solution: FALSE. ( Var ( X ) ≥ 0) ♦ 3. Suppose X has m.g.f. M X ( t ) = 0 . 2 e t + 0 . 8. Find Var ( X ). Solution: If M X ( t ) = pe t + q ⇒ X ∼ Bern( p ) ⇒ Var ( X ) = pq Thus, X ∼ Bern(0 . 2) in this example ⇒ Var ( X ) = 0 . 2 * . 8 = 0 . 16 ♦ 4. TRUE or FALSE? If the correlation between X and Y is 0, then X and Y are independent. Solution: FALSE. ♦ 5. Suppose that X and Y are independent Exponential( λ ) random variables. Find Var ( XY ) (yup — the variance of the product)....
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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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