Chapter 5 ans

Chapter 5 ans - Chapter 05 - Discrete Random Variables...

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Chapter 05 - Discrete Random Variables 5-1 CHAPTER 5—Discrete Random Variables 5.1 A random variable is a variable that assumes numerical values determined by the outcome of an experiment. LO1 5.2 The values of a discrete random variable can be counted, or listed; the values of a continuous random variable cannot be counted, or listed. LO1 5.3 a. Discrete b. Discrete c. Continuous d. Discrete e. Discrete f. Continuous g. Continuous LO1 5.4 The probability distribution of a discrete random variable is a table, graph, or formula that gives the probability associated with each possible value that the random variable can assume. LO2 5.5 The probability of each possible outcome is > 0, and the sum of the probabilities of all possible outcomes is 1. LO2 5.6 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 . The standard deviation is the square root of the probability weighted sum of the squared deviations from the mean. LO2 5.7 The standard deviation measures the spread of the population of the random variable. LO2
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Chapter 05 - Discrete Random Variables 5-2 5.8 a. Valid b. Not valid; 1 2 1 p c. Not valid; p ( x ) .9 all x d. Valid LO2 5.9 a. x = 0(.2) + 1(.8) = .8 2 x = (0 – .8) 2 (.2) + (1 – .8) 2 (.8) = .16 x = 4 . 0 16 . LO2 b. 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 9097 . 8275 . x c. 6 . 1 ) 2 (. 5 ) 4 (. 2 ) 3 (. 0 ) 1 (. 2 x 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 Since the probabilities sum to 1.00, u x is the mean of all possible observed values of x. LO2
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Chapter 05 - Discrete Random Variables 5-3 5.10 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 LO2 5.11 a.    667 . 444 . 444 . 9 1 6 . 2 9 4 6 . 1 9 4 6 . 0 667 . 9 1 2 9 4 1 9 4 0 x 2 2 2 2 x x [ x 2 x ] [.667 2(.667)] [–.667, 2.001] contains at least 3 4 of the observed values of x . [ x 3 x ] [.667 3(.667)] [–1.334, 2.668] contains at least 8 9 of the observed values of x . b.
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This note was uploaded on 08/26/2011 for the course AGS 4401 taught by Professor Henry during the Spring '11 term at FIU.

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Chapter 5 ans - Chapter 05 - Discrete Random Variables...

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