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Unformatted text preview: Chapter 5 Discrete Probability Distributions Solutions: 1. a. Head, Head (H,H) Head, Tail (H,T) Tail, Head (T,H) Tail, Tail (T,T) b. x = number of heads on two coin tosses c. Outcome Values of x (H,H) 2 (H,T) 1 (T,H) 1 (T,T) d. Discrete. It may assume 3 values: 0, 1, and 2. 6. a. values: 0,1,2,...,20 discrete b. values: 0,1,2,... discrete c. values: 0,1,2,...,50 discrete d. values: 0 x 8 continuous e. values: x &gt; continuous 7. a. f ( x ) 0 for all values of x . f ( x ) = 1 Therefore, it is a proper probability distribution. b. Probability x = 30 is f (30) = .25 c. Probability x 25 is f (20) + f (25) = .20 + .15 = .35 d. Probability x &gt; 30 is f (35) = .40 12. a. Yes; f ( x ) 0 for all x and f ( x ) = .15 + .20 + .30 + .25 + .10 = 1 b. P(1200 or less) = f (1000) + f (1100) + f (1200) = .15 + .20 + .30 = .65 13. a. Yes, since f ( x ) 0 for x = 1,2,3 and f ( x ) = f (1) + f (2) + f (3) = 1/6 + 2/6 + 3/6 = 1 b. f (2) = 2/6 = .333 c. f (2) + f (3) = 2/6 + 3/6 = .833 17. a/b. x f ( x ) x f ( x ) x ( x ) 2 ( x ) 2 f ( x ) .10 .002.45 6.0025 .600250 1 .15 .151.45 2.1025 .315375 2 .30 .60 .45 .2025 .060750 3 .20 .60 .55 .3025 .060500 4 .15 .60 1.55 2.4025 .360375 5 .10 .50 2.55 6.5025 .650250 2.45 2.047500 E ( x ) = = 2.45 2 = 2.05 = 1.43 19. a. E ( x ) = x f ( x ) = 0 (.56) + 2 (.44) = .88 b. E ( x ) = x f ( x ) = 0 (.66) + 3 (.34) = 1.02 c. The expected value of a 3  point shot is higher. The expected value of a 3  point shot is higher....
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This note was uploaded on 02/01/2011 for the course STAT 101 taught by Professor Oba during the Fall '10 term at Athens University of Econ and Bus.
 Fall '10
 oba
 Statistics, Probability

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