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The generalized negative binomial pmf is given by Let X,

Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye ISBN: 9780321629111 32

Solution for problem 114E Chapter 3

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Problem 114E

The generalized negative binomial pmf is given by Let X, the number of plants of a certain species found in a particular region, have this distribution with p = .3 and r =2.5. What is P( X = 4)? What is the probability that at least one plant is found?

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Answer: Step1: Given, the negative binomial pmf is given by r x nb(x;r,p) = k(r,x). p (1 p) ; x = 0,1,2…. ------- (1) Let ‘x’ be the number of plants of a certain species found in a particular region. Given, p = 0.3 and r = 2.5. i). To find P(x = 4). k(r , x) = (x + r1)(x +r2)......(x +rx) x! Substitute this in equation (1) Therefore, (x + r1)(x +r2)......(x +rxr x nb(x;r,p) = x! p (1 p) (4+2.51)(4+2.52)(4+2.53)(4+2.54) 2.5 4 P(x = 4) = 4! (0.3) (1 0.3) = (5.5)(4.5)(3.5)(2.(0.0118) 4! = 0.1065. Step2: ii). To calculate what is the probability that at least one plant is found. P( at least one plant) = 1- P( zero plant) = 1- P(x = 0) 2.5 0 = 1 - k(2.5,0)(0.3) (1 0.3) = 1- 0.0493 ( Here, k(r , 0) = 1.) = 0.9507. Therefore, P(x = 4) = 0.1065 and the probability that at least one plant is 0.9507.

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Chapter 3, Problem 114E is Solved
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Textbook: Probability and Statistics for Engineers and the Scientists
Edition: 9
Author: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye
ISBN: 9780321629111

Since the solution to 114E from 3 chapter was answered, more than 426 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 114E from chapter: 3 was answered by , our top Statistics solution expert on 05/06/17, 06:21PM. This textbook survival guide was created for the textbook: Probability and Statistics for Engineers and the Scientists, edition: 9. This full solution covers the following key subjects: found, Negative, binomial, Generalized, given. This expansive textbook survival guide covers 18 chapters, and 1582 solutions. The answer to “The generalized negative binomial pmf is given by Let X, the number of plants of a certain species found in a particular region, have this distribution with p = .3 and r =2.5. What is P( X = 4)? What is the probability that at least one plant is found?” is broken down into a number of easy to follow steps, and 50 words. Probability and Statistics for Engineers and the Scientists was written by and is associated to the ISBN: 9780321629111.

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The generalized negative binomial pmf is given by Let X,