Chap006 - CHAPTER 6 DISCRETE PROBABILITY DISTRIBUTIONS 1...

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C HAPTER 6 D ISCRETE P ROBABILITY D ISTRIBUTIONS 1. Mean = 1.3 Variance = 0.81 found by: ( ) 0(.20) 1(.40) 2(.30) 3(.10) 1.3 XP X μ = = + + + = 2 2 2 2 2 2 ( ) ( ) (0 1.3) (0.2) (1 1.3) (0.4) (2 1.3) (0.3) (3 1.3) (0.1) 0.81 X P X σ μ = - = - + - + - + - = 2. Mean = 5.4 Variance = 12.04 found by: ( ) 2(.5) 8(.3) 10(.2) 5.4 XP X μ = = + + = 2 2 2 2 2 ( ) ( ) (2 5.4) (.5) (8 5.4) (.3) (10 5.4) (.2) 12.04 X P X σ μ = - = - + - + - = 3. a. The second or middle, one b. 0.20, 0.40, 0.90 c. μ = 14.5, 5(.1) 10(.3) 15(.2) 20(.4) 14.5 + + + = Variance = 27.25 2 2 2 2 2 (5 14.5) (.1) (10 14.5) (.3) (15 14.5) (.2) (20 14.5) (.4) 27.25 σ = - + - + - + - = σ = 5.22 found by 27.25 4. a. Discrete b. Continuous c. Discrete d. Continuous e. Discrete f. Continuous 5. 0(.3) 1(.4) 2(.2) 3(.1) 1.1 μ = + + + = 2 2 2 2 2 (0 1.1) (.3) (1 1.1) (.4) (2 1.1) (.2) (3 1.1) (.1) 0.89 σ = - + - + - + - = σ = 0.943 6. 1000(.6) 1200(.3) 1500(.1) 1110 μ = + + = 2 2 2 2 (1000 1110) (.6) (1200 1110) (.3) (1500 1110) (.1) 24,900 σ = - + - + - = σ = 157.8 7. a. 0.20 b. 0.55 c. 0.95 d. 0(.45) 10(.3) 100(.2) 500(0.05) 48 μ = + + + = 2 2 2 2 2 (0 48) (.45) (10 48) (.3) (100 48) (.2) (500 48) (.05) 12,226 σ = - + - + - + - = σ = 110.57 Chapter 6 53
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8. a. 0.5000 b. 0.6667 c. 0 d. 0(1/3) 1(1/ 2) 2(0) 3(1/6) 1 μ = + + + = 2 2 2 2 2 (0 1) (1/3) (1 1) (1/ 2) (2 1) (0) (3 1) (1/6) 1 σ = - + - + - + - = σ = 1 9. a. 2 4 2 4! P(2) (.25) (.75) 0.2109 2!(4 2)! - = = - b. 3 4 3 4! P(3) (.25) (.75) 0.0469 3!(4 3)! - = = - 10. a. 1 5 1 5! P(1) (.4) (.6) 0.2592 1!(5 1)! - = = - b. 2 5 2 5! P(2) (.4) (.6) 0.3456 2!(5 2)! - = = - 11. a. x P(X) 0 0.064 1 0.288 2 0.432 3 0.216 b. 0(0.064) ...3(0.216) 1.8 μ = + = 2 2 2 (0 1.8) 0.064 ... (3 1.8) 0.216 0.72 σ = - + + - = 0.72 0.8485 σ = = 12. a. x P(x) 0 0.168 1 0.360 2 0.309 3 0.132 4 0.028 5 0.002 b. 0(0.168) ... 5(0.002) 1.5 μ = + + = 2 2 2 (0 1.5) 0.168 ... (5 1.5) 0.002 1.05 σ = - + + - = 1.05 1.0247 σ = = 13. a. 0.2668, found by 2 7 9! P(2) (.3) (.7) 2!(9 2)! = - b. 0.1715, found by 4 5 9! P(4) (.3) (.7) 4!(9 4)! = - c. 0.0404, found by 0 9 9! P(0) (.3) (.7) 0!(9 0)! = - Chapter 6 54
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14. a. 0.7351, found by 6 0 6! P(6) (.95) (.05) 6!(6 6)! = - b. 0.2321, found by 5 1 6! P(5) (.95) (.05) 5!(6 5)! = - c. μ = 5.7, found by 6(.95) d. 2 0.285 σ = , found by 6(.95)(.05), 0.285 0.5339 σ = = 15. a. 0.2824, found by 0 12 12!
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