Explanation Given information: f ( x ) = 2 ( x − 1 ) , 1 ≤ x ≤ 2 And Pr ( 1.5 ≤ X ≤ 1.7 ) Formula used: 1) Sum rule of integration : ∫ f ( x ) ± g ( x ) d x = ∫ f ( x ) d x ± ∫ g ( x ) d x 2) Power rule of integration: ∫ x n d x = x n + 1 n + 1 , n ≠ − 1 3) Area under the graph of f ( x ) is given by a definite integral P ( a ≤ X ≤ b ) = ∫ a b f ( x ) d x Calculation: The probability that X lies between the endpoints of the given interval [ a , b ] is given by the area under the graph of a function f ( x ) from a to b So, area under the graph of f ( x ) is given by a definite integral P ( a ≤ X ≤ b ) = ∫ a b f ( x ) d x Thus, Pr ( 1.5 ≤ X ≤ 1.7 ) = ∫ 1.5 1.7 f ( x ) d x = ∫ 1.5 1.7 2 ( x − 1 ) d x ⇒ ∫ 1.5 1.7 2 ( x − 1 ) d x = ∫ 1.5 1.7 ( 2 x − 2 ) d x Applying the sum rule of integration, ⇒ ∫ 1.5 1.7 2 ( x − 1 ) d x = ∫ 1.5 1.7 2 x d x − ∫ 1

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ISBN: 9780137590810

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

Publisher: PEARSON

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Chapter 12.2, Problem 16E

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To calculate: The probability Pr ( 1.5 ≤X ≤ 1.7) for function f(x)= 2 (x−1), 1≤x≤2

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Chapter 12.2, Problem 15E

Chapter 12.2, Problem 17E

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The probability Pr ( 1.5 ≤ X ≤ 1.7 ) for function f ( x ) = 2 ( x − 1 ) , 1 ≤ x ≤ 2

Solution Summary: The author explains that the probability that X lies between the endpoints of the given interval is given by a definite integral.

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To calculate: The probability Pr ( 1.5 ≤X ≤ 1.7) for function f(x)= 2 (x−1), 1≤x≤2

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Chapter 12 Solutions