Explanation Given information: The quartiles of the probability function to be those values a 1 , a 2 , a 3 such that P ( − ∞ < x ≤ a 1 ) = P ( a 1 ≤ x ≤ a 2 ) = P ( a 2 ≤ x ≤ a 3 ) = P ( a 3 ≤ x < ∞ ) = 1 4 . Formula used : P ( a ≤ x ≤ b ) = ∫ a b p ( x ) d x Calculation: Let us consider the probability function. ∫ 1 1 + x 2 d x = tan − 1 x By given condition P ( − ∞ < x ≤ a 1 ) = P ( a 1 ≤ x ≤ a 2 ) = P ( a 2 ≤ x ≤ a 3 ) = P ( a 3 ≤ x < ∞ ) = 1 4 For the value of a 1 , P ( − ∞ < x ≤ a 1 ) = 1 4 ⇒ ∫ − ∞ a 1 p ( x ) d x = 1 4 ⇒ ∫ − ∞ a 1 1 1 + x 2 d x = 1 4 ⇒ ( tan − 1 x ) − ∞ a 1 = 1 4 ⇒ ( tan − 1 a 1 − tan − 1 ( − ∞ ) ) = 1 4 ⇒ ( tan − 1 a 1 − ( − π 2 ) ) = 1 4 ⇒ ( tan − 1 a 1 + π 2 ) = 1 4 ⇒ tan − 1 a 1 = 1 4 − π 2 ⇒ a 1 = tan ( 1 4 − π 2 ) ⇒ a 1 = − 3.9163 For the value of a 2 P ( a 1 ≤ x ≤ a 2 ) = 1 4 ⇒ P ( − 3

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 8.8, Problem 24E

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To find:The quartile values a1,a2,a3 for the probability function p(x)=11+x2 .

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Chapter 8.8, Problem 23E

Chapter 8.8, Problem 25E

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Chapter 8 Solutions

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Ch. 8.1 - Prob. 1PQ Ch. 8.1 - Prob. 2PQ Ch. 8.1 - Prob. 3PQ Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E

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The quartile values a 1 , a 2 , a 3 for the probability function p ( x ) = 1 1 + x 2 .

Solution Summary: The author explains the quartile values of the probability function p(x) = 11,a_2, and the formula used to calculate it.

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To find:The quartile values a1,a2,a3 for the probability function p(x)=11+x2 .

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Chapter 8 Solutions