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Chap004 - CHAPTER 4 Discrete Random Variables 4.1 4.2 4.3...

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CHAPTER 4 – Discrete Random Variables 4.1 See page 153 in text. 4.2 The values of a discrete random variable can be counted, or listed; the values of a continuous random variable cannot be counted, or listed. 4.3 a. Discrete b. Discrete c. Continuous d. Discrete e. Discrete f. Continuous g. Continuous 4.4 See page 154 in text. 4.5 See page 156 in text. The probability of each possible outcome is > 0, and the sum of the probabilities of all possible outcomes is 1. 4.6 See page 157 in text. The mean is the sum of each possible value of x multiplied by the probability of that value of x . This represents the mean expected value of x . 4.7 See page 160 in text. The standard deviation measures the spread of the population of the random variable. 4.8 a. Valid b. Not valid; p 1 2 ( 29 = –1 c. Not valid; p ( x ) = .9 all x d. Valid 4.9 a. x μ = 0(.2) + 1(.8) = .8 2 x σ = (0-.8) 2 (.2) + (1-.8) 2 (.8) = .16 x σ = 4 . 0 16 . = b. μ x = xp ( x ) all x = 0(.25) + 1(.45) + 2(.2) + 3(.1) = 1.15 8275 . ) 1 (. ) 15 . 1 3 ( ) 2 (. ) 15 . 1 2 ( ) 45 (. ) 15 . 1 1 ( ) 25 (. ) 15 . 1 0 ( 2 2 2 2 2 = - + - + - + - = x σ 9097 . 8275 . = = x σ 47
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Chapter 4: Discrete Random Variables c. 6 . 1 ) 2 (. 5 ) 4 (. 2 ) 3 (. 0 ) 1 (. 2 = + + + - = x μ 1071 . 2 44 . 4 44 . 4 ) 2 (. ) 6 . 1 5 ( ) 4 (. ) 6 . 1 2 ( ) 3 (. ) 6 . 1 0 ( ) 1 (. ) 6 . 1 2 ( 2 2 2 2 2 = = = - + - + - + - - = x x σ σ Since the probabilities sum to 1.00, u x is the mean of all possible observed values of x. 4.10 a. x 0 1 2 p ( x ) 9 4 9 4 9 1 b. x 0 1 2 3 p ( x ) 8 1 8 3 8 3 8 1 c. x 0 1 2 3 4 p ( x ) 16 1 4 1 8 3 4 1 16 1 4.11 a. [ μ x ± 2 σ x ] = [.667 ± 2(.667)] = [–.667, 2.001] contains at least 3 4 of the observed values of x . [ μ x ± 3 σ x ] = [.667 ± 3(.667)] = [–1.334, 2.668] contains at least 8 9 of the observed values of x . b. See the methods outlined in part a. μ x = 1.5 σ x 2 = .75 σ x = .866 [ μ x ± 2 σ x ] = [–.232, 3.232] [ μ x ± 3 σ x ] = [–1.098, 4.098] c. See the methods outlined in part (a). μ x = 2 σ x 2 = 1 σ x = 1 [ μ x ± 2 σ x ] = [0, 4] [ μ x ± 3 σ x ] = [–1, 5] 4.12 a. x 1 2 3 4 5 p ( x ) 15 1 15 2 5 1 15 4 3 1 48
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Chapter 4: Discrete Random Variables b. p ( x ) 0 for each value of x . p ( x ) all x = 1 15 + 2 15 + 1 5 + 4 15 + 1 3 = 1 c. d. 4.13 a. Graph not included in this manual.
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