Explanation Approach: If x is a continuous random variable with probability density function f on [ a , b ] , then the expected value of x is: E ( x ) = μ = ∫ a b x f ( x ) d x The variance of x is: Var ( x ) = ∫ a b ( x − μ ) 2 f ( x ) d x and the standard deviation of x is: σ = Var ( x ) Calculation: Consider the given probability density function, f ( x ) = 4 x 5 ; x ≥ 1 The expected value is E ( x ) = ∫ 0 ∞ x f ( x ) d x = lim a → ∞ ∫ 1 a x ( 4 x 5 ) d x<

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ISBN: 9780321964038

Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher: Pearson Addison Wesley,

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Chapter 13.2, Problem 2YT

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The variance for the given probability density function f(x)=4x5 for x≥1 by using its alternative formula.

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Chapter 13.2, Problem 1YT

Chapter 13.2, Problem 3YT

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The variance for the given probability density function f ( x ) = 4 x 5 for x ≥ 1 by using its alternative formula.

Solution Summary: The author calculates the expected value and variance for the given probability density function 43 and 0.22.

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To find:

The variance for the given probability density function f(x)=4x5 for x≥1 by using its alternative formula.

Want to see the full answer?

Chapter 13 Solutions

The variance for the given probability density function f ( x ) = 4 x 5 for x ≥ 1 by using its alternative formula.

Solution Summary: The author calculates the expected value and variance for the given probability density function 43 and 0.22.

Concept explainers

Videos

To find: The variance for the given probability density function f(x)=4x5 for x≥1 by using its alternative formula.

Want to see the full answer?

Chapter 13 Solutions

To find:

The variance for the given probability density function f(x)=4x5 for x≥1 by using its alternative formula.