Explanation Given information: The variable X follows the geometric distribution with parameter p = 0.6 . Explanation: The variable X follows the geometric distribution with parameter p = 0.6 . Where X is the number of successes that precede the first failure, that is, X takes values from 0 , 1 , 2 , ... and so on. Failure occurs at the first trial, which means there are 0 successes before the first failure. 0 successes can be represented by X = 0 , and the probability is, p 0 = Pr ( X = 0 ) = 1 − p . To find p 0 , substitute n = 0 and p = 0.6 in p 0 = 1 − p . p 0 = 1 − 0.6 = 0.4 Failure occurs at the second trial, which means, there is success before the first failure. 1 success can be represented by X = 1 and the probability is, p 1 = Pr ( X = 1 ) = p ( 1 − p ) . To find p 1 , substitute n = 1 and p = 0.6 in p 1 = p ( 1 − p ) . ⇒ p 1 = 0.6 ( 1 − 0.6 ) = 0.24 Next, Failure occurs at the third trial, which means, there are 2 successes before the first failure. 2 successes can be represented by X = 2 and the probability is, p 2 = Pr ( X = 2 ) = p 2 ( 1 − p ) . To find p 2 , substitute n = 2 and p = 0.6 in p 2 = p 2 ( 1 − p ) . ⇒ p 2 = ( 0.6 ) 2 ( 1 − 0.4 ) = 0.144 Next, failure occurs at the fourth trial, which means, there are 3 successes before the first failure. 3 successes can be represented by X = 3 and the probability is, p 3 = Pr ( X = 3 ) = p 3 ( 1 − p ) . To find p 3 , substitute n = 3 and p = 0

Student Solutions Manual for Calculus & Its Applications and Calculus & Its Applications, Brief Version

14th Edition

ISBN: 9780134463230

Author: Larry J. Goldstein, David I Lay, David I. Schneider, Nakhle H. Asmar

Publisher: PEARSON

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Chapter 12.5, Problem 11E

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The geometric probabilities p0,....,p5 and make a histogram, if X is a geometric random variable with parameter p=.6.

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Chapter 12.5, Problem 10E

Chapter 12.5, Problem 12E

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Chapter 12 Solutions

Student Solutions Manual for Calculus & Its Applications and Calculus & Its Applications, Brief Version

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The geometric probabilities p 0 , .... , p 5 and make a histogram, if X is a geometric random variable with parameter p = .6 .

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Chapter 12 Solutions