Explanation Given information: The density function f ( x ) = 1 2 π e − ( 1 / 2 ) ( x − 4 ) 2 . Explanation: Let X be a random variable with normal density function f ( x ) = 1 σ 2 π e − ( 1 / 2 ) [ ( x − μ ) / σ ] 2 . Then, the expected value and standard deviation of X are given by μ and σ respectively. The given normal density function is f ( x ) = 1 2 π e − ( 1 / 2 ) ( x − 4 ) 2 , which can be written as f ( x ) =

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Chapter 12.4, Problem 15E

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The expected value and the standard deviation (by inspection) of the normal random variable with the density function 12πe−(1/2)(x−4)2.

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Chapter 12.4, Problem 14E

Chapter 12.4, Problem 16E

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The expected value and the standard deviation (by inspection) of the normal random variable with the density function 1 2 π e − ( 1 / 2 ) ( x − 4 ) 2 .

Solution Summary: The author analyzes the density function f(x)=1sqrt2pi e

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The expected value and the standard deviation (by inspection) of the normal random variable with the density function 12πe−(1/2)(x−4)2.

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Chapter 12 Solutions