Explanation Given information: The probability density function is p ( x ) = C ln x on [ 1 , e ] . Formula used: If p is a probability density function for X , then it is a continuous function such that P ( a ≤ X ≤ b ) = ∫ a b p ( x ) d x . Also a probability function p ( x ) must satisfy two conditions such that p ( x ) ≥ 0 for all x ∫ − ∞ ∞ p ( x ) d x = 1 Calculation: A probability density function p ( x ) must satisfy ∫ − ∞ ∞ p ( x ) d x = 1 . p ( x ) = C ln x (Given) So, ∫ − ∞ ∞ p ( x ) d x = 1 ⇒ ∫ 1 e C ln x d x = 1 ⇒

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 9.1, Problem 6E

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To find: The constant C and also compute the value of P(1≤X≤2) .

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Chapter 9.1, Problem 5E

Chapter 9.1, Problem 7E

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The constant C and also compute the value of P ( 1 ≤ X ≤ 2 ) .

Solution Summary: The author explains the probability density function p(x)=Cmathrmlnx, which is a continuous function.

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To find: The constant C and also compute the value of P(1≤X≤2) .

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Chapter 9 Solutions