Explanation Given information: A random variable X follows Poisson distribution with parameter λ = 2.5 . Explanation: A Poisson random variable X whose values are discrete numbers 0 , 1 , 2 , ... . A random variable X follows Poisson distribution with parameter λ = 2.5 . Now, find probabilities p 0 , p 1 , p 2 , p 3 , p 4 , p 5 , and p 6 by using Poisson distribution formula as follows: p n = λ n n ! e − λ . To find p 0 , substitute n = 0 and λ = 2.5 in p n = λ n n ! e − λ . p 0 = Pr ( X = 0 ) p 0 = ( 2.5 ) 0 0 ! e − 2.5 p 0 = e − 2.5 p 0 = 0.082085 ≈ 0.0821 Thus, p 0 = 0.0821 . To find p 1 , substitute n = 1 and λ = 2.5 in p n = λ n n ! e − λ . p 1 = Pr ( X = 1 ) p 1 = ( 2.5 ) 1 ! e − 2.5 p 1 = 0.205212 ≈ 0.2052 Thus, p 1 = 0.2052 . To find p 2 , substitute n = 2 and λ = 2.5 in p n = λ n n ! e − λ . p 2 = Pr ( X = 2 ) p 2 = ( 2.5 ) 2 2 × 1 e − 2.5 Simplifying, p 2 = 0.256516 ≈ 0.2565 Thus, p 2 = 0.2565 . To find p 3 , substitute n = 3 and λ = 2.5 in p n = λ n n ! e − λ . p 3 = Pr ( X = 3 ) p 3 = ( 2.5 ) 3 3 ! e − 2.5 Simplifying, p 3 = ( 2

Calculus & Its Applications (14th Edition)

14th Edition

ISBN: 9780134437774

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

Publisher: PEARSON

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Chapter 12.5, Problem 4E

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The Poisson probabilities p0,.....,p6 to four decimal places with λ=2.5 and make a histogram.

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Chapter 12.5, Problem 3E

Chapter 12.5, Problem 5E

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Chapter 12 Solutions

Calculus & Its Applications (14th Edition)

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Ch. 12.1 - Decision Making Based on Expected Value A citrus...Ch. 12.1 - Prob. 10E Ch. 12.2 - Prob. 1CYU Ch. 12.2 - Prob. 2CYU Ch. 12.2 - Prob. 1E Ch. 12.2 - Prob. 2E Ch. 12.2 - Prob. 3E Ch. 12.2 - Prob. 4E Ch. 12.2 - Prob. 5E Ch. 12.2 - Prob. 6E Ch. 12.2 - Prob. 7E Ch. 12.2 - Prob. 8E Ch. 12.2 - Prob. 9E Ch. 12.2 - Prob. 10E Ch. 12.2 - Prob. 11E Ch. 12.2 - Prob. 12E Ch. 12.2 - Prob. 13E Ch. 12.2 - Prob. 14E Ch. 12.2 - Prob. 15E Ch. 12.2 - Prob. 16E Ch. 12.2 - Prob. 17E Ch. 12.2 - Prob. 18E Ch. 12.2 - Prob. 19E Ch. 12.2 - Prob. 20E Ch. 12.2 - Prob. 21E Ch. 12.2 - Prob. 22E Ch. 12.2 - Prob. 23E Ch. 12.2 - Prob. 24E Ch. 12.2 - Prob. 25E Ch. 12.2 - Prob. 26E Ch. 12.2 - An experiment consists of selecting a point at...Ch. 12.2 - Prob. 28E Ch. 12.2 - Prob. 29E Ch. 12.2 - Prob. 30E Ch. 12.2 - Prob. 31E Ch. 12.2 - Prob. 32E Ch. 12.2 - Prob. 33E Ch. 12.2 - Prob. 34E Ch. 12.2 - Prob. 35E Ch. 12.2 - A random variable X has a cumulative distribution...Ch. 12.2 - Prob. 37E Ch. 12.2 - Prob. 38E Ch. 12.3 - 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The Poisson probabilities p 0 , ..... , p 6 to four decimal places with λ = 2.5 and make a histogram.

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