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# PracticeQuestions3Answers - 1 B 2 D 3 a 0.16 0.14 0.04 =...

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1. B 2. D 3. a. 0.16 + 0.14 + 0.04 = 0.34 b. 0.17 + 0.16 = 0.33 c. 0.23 + 0.17 + 0.16 + 0.14 + 0.04 = 0.74 d. 1 – P ( X = 6) = 1 – 0.04 = 0.96 4. ( ) X x xP x μ = = 2.97 2 2 2 2 ( ) 11.49 (2.97) 2.6691 X X x x P x σ μ = - = - = ; hence 1.6337 x σ = 5. λ = 4.2 , P ( X = 3) = 0.185 6. λ = nP = 7.5, then P ( X >3) = 1 – P ( X 3) = 1 – (0.0006+0.0041+ 0.0156 + 0.0389) = 0.94 7. Cov( , ) ( , ) X Y X Y xyP x y μ μ = - ∑∑ = 4.73 – (2.1)(2.15) = 0.215 8. a. ANSWER: x 1 2 3 P ( x ) 0.17 0.38 0.45 b. ANSWER: ( 29 2.28 X x P x μ = = c. ANSWER: ( 29 ( 29 2 2 2 2 5.74 2.28 0.5416 X X x P x σ μ = - = - = . Hence, X σ =0.7359.

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d. ANSWER: y 0 1 2 P ( y ) 0.28 0.26 0.46 e. ANSWER: ( 29 1.18 Y y P y μ = f. ANSWER: ( 29 ( 29 2 2 2 2 2.10 1.18 0.7076 Y Y y P y σ μ = - = - = . Hence, 0.8412 Y σ = . g. ANSWER: Cov( X , Y )= ( 29 , X Y x y xyP x y μ μ - ∑∑ =2.94-(2.28)(1.18)=0.2496 h. ANSWER: ρ = Corr( X , Y ) = ( 29 ( 29 ( 29 Cov , 0.2496 0.4032 0.7359 0.8412 X Y x y σ σ = = i. ANSWER: 2 W X Y μ μ μ = + =2(2.28)+1.18 = 5.74 j.
ANSWER: ( 29 ( 29 2 2 2 2 2 2 1 W X Y σ σ σ = + +2(2)(1)Cov( X , Y ) = 4(0.5416) + 0.7076 + 4(0.2496) = 3.8724 k. ANSWER: The variables X and Y are not statistically independent since P ( X =1) = 0.17, P ( Y = 0) = 0.28, and P ( X =1 and Y = 0) = 0.10 P ( X = 1) P ( Y = 0). 9. a. A b. C 10. a. B b. D 11. a. D b. B c. A d. C 12. C 13. A 14. C 15. D 16. A 17. a. B b. D 18. C 19 a. C b. B c. A d. D 20. A 21. C 22. B 23. C 24. D 25. C 26. A 27. A 28. B

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29. A 30. A 31. B 32. C 33. A 34.
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PracticeQuestions3Answers - 1 B 2 D 3 a 0.16 0.14 0.04 =...

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