Explanation Given information: f ( x ) = 1 4 , 1 ≤ x ≤ 5 and Pr ( X ≤ 3 ) Formula used: 1) Power rule of integration : ∫ x n d x = x n + 1 n + 1 , n ≠ − 1 2) 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 As the function f ( x ) is defined for interval 1 ≤ x ≤ 5 , Pr ( X ≤ 3 ) = Pr ( 1 ≤ X ≤ 3 )

12th Edition

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 17E

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To calculate: The probability Pr ( X ≤ 3) for the given function f(x)= 14, 1≤x≤5.

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Chapter 12.2, Problem 16E

Chapter 12.2, Problem 18E

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The probability Pr ( X ≤ 3 ) for the given function f ( x ) = 1 4 , 1 ≤ x ≤ 5 .

Solution Summary: The author explains how the probability of X lies between the endpoints of the given interval [a,b] is given by a definite integral.

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To calculate: The probability Pr ( X ≤ 3) for the given function f(x)= 14, 1≤x≤5.

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Chapter 12 Solutions