Explanation Given information: p ( x ) = 3 x − 4 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 The mean value is μ = ∫ − ∞ ∞ x . p ( x ) d x Solution: A probability density function p ( x ) must satisfy ∫ − ∞ ∞ p ( x ) d x = 1 . p ( x ) = 3 x − 4 (Given) ∫ − ∞ ∞ p ( x ) d x = ∫ 1 ∞ 3 x − 4 d x = 3 ∫ 1 ∞ x − 4 d x = 3 [ x − 4 + 1 − 4 + 1 ] 1 ∞ = 3 [ x

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Chapter 9.1, Problem 9E

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To verify: The function p(x)=3x−4 is a probability density function on [1,∞) and also calculate its mean value.

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Chapter 9.1, Problem 8E

Chapter 9.1, Problem 10E

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To verify: The function p ( x ) = 3 x − 4 is a probability density function on [ 1 , ∞ ) and also calculate its mean value.

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To verify: The function p(x)=3x−4 is a probability density function on [1,∞) and also calculate its mean value.

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Chapter 9 Solutions