Explanation Given Information: The function, f ( x ) = 0.2 e − 0.2 x over the interval [ 0 , ∞ ) . Proof: Consider the function, f ( x ) = 0.2 e − 0.2 x A function f of a continuous random variables x whose set of values is the interval [ a , b ] . The function is a probability density function when it is non-negative and continuous on the interval [ a , b ] and when ∫ a b f ( x ) d x = 1 f ( x ) is non-negative and continuous over the interval [ 0 , ∞ ) Now, evaluate ∫ a b f ( x ) d x as, ∫ 0 ∞ f ( x ) d x = ∫ 0 ∞ 0.2 e − 0.2 x d x = 0.2 ∫ 0 ∞ e − 0.2 x d x = 0

Calculus: An Applied Approach (MindTap Course List)

10th Edition

ISBN: 9781305860919

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 9.2, Problem 6E

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To prove: The function, f(x)=0.2e−0.2x is a probability density function over the interval [0,∞).

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Chapter 9.2, Problem 5E

Chapter 9.2, Problem 7E

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Chapter 9 Solutions

Calculus: An Applied Approach (MindTap Course List)

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To prove: The function, f ( x ) = 0.2 e − 0.2 x is a probability density function over the interval [ 0 , ∞ ) .

Solution Summary: The author explains the function, f(x)=0.2e-0.2x, which is a probability density function.

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To prove: The function, f(x)=0.2e−0.2x is a probability density function over the interval [0,∞).

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Chapter 9 Solutions