Explanation Given information: f ( x ) = k A k x k + 1 , x ≥ A , where k and A are any positive constants. Cumulative distribution function F ( x ) is called a Pareto distribution. Explanation: Since k and A are positive constants, f ( x ) = k A k x k + 1 ≥ 0 for all x ≥ A , The given function is probability density function if it satisfies theconditionbelo:. ∫ A ∞ f ( x ) d x = 1 for x ≥ A . Now solve ∫ A ∞ f ( x ) d x . Substitute the given function f ( x ) = k A k x k + 1 . ∫ A ∞ f ( x ) d x = ∫ A ∞ k A k x k + 1 d x Take the constant k A k outside the integral. ⇒ ∫ A ∞ k A k x k + 1 d x = k A k ∫ A ∞ 1 x k + 1 d x . ⇒ ∫ A ∞ k A k x k + 1 d x = k A k lim b → ∞ ∫ A b 1 x k + 1 d x Using power rule of integration, ∫ x n d x = x n + 1 n + 1 , n ≠ − 1

12th Edition

ISBN: 9780137590810

Author: Larry J. Goldstein, David C. Lay, David I. Schneider, Nakhle H. Asmar, William Edward Tavernetti

Publisher: PEARSON

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Chapter 12, Problem 4RE

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Whether the function f(x)=kAkxk+1, x≥A, k>0, A>0 is a density function and compute F(x).

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Whether the function f ( x ) = k A k x k + 1 , x ≥ A , k > 0 , A > 0 is a density function and compute F ( x ) .

Solution Summary: The author explains that the given function f(x)=kAxK+1 is a probability density function.

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Whether the function f(x)=kAkxk+1, x≥A, k>0, A>0 is a density function and compute F(x).

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Chapter 12 Solutions

Whether the function f ( x ) = k A k x k + 1 , x ≥ A , k &gt; 0 , A &gt; 0 is a density function and compute F ( x ) .

Solution Summary: The author explains that the given function f(x)=kAxK+1 is a probability density function.

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Whether the function f(x)=kAkxk+1, x≥A, k>0, A>0 is a density function and compute F(x).

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Chapter 12 Solutions

Whether the function f ( x ) = k A k x k + 1 , x ≥ A , k > 0 , A > 0 is a density function and compute F ( x ) .