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

MyLab Math with Pearson eText -- 24 Month Access -- for Calculus & Its Applications

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ISBN: 9780137590469

Author: Larry Goldstein / David Lay

Publisher: Pearson Education (US)

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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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Chapter 12, Problem 3RE

Chapter 12, Problem 5RE

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Chapter 12 Solutions

MyLab Math with Pearson eText -- 24 Month Access -- for Calculus & Its Applications

Ch. 12.1 - Compute the expected value and the variance of the...Ch. 12.1 - Prob. 2CYU Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - Probability Table, Expected Value The number of...Ch. 12.1 - Prob. 7E Ch. 12.1 - Prob. 8E

Ch. 12.1 - Decision Making Based on Expected Value A citrus...Ch. 12.1 - Prob. 10E Ch. 12.2 - Prob. 1CYU Ch. 12.2 - Prob. 2CYU Ch. 12.2 - Prob. 1E Ch. 12.2 - Prob. 2E Ch. 12.2 - Prob. 3E Ch. 12.2 - Prob. 4E Ch. 12.2 - Prob. 5E Ch. 12.2 - Prob. 6E Ch. 12.2 - Prob. 7E Ch. 12.2 - Prob. 8E Ch. 12.2 - Prob. 9E Ch. 12.2 - Prob. 10E Ch. 12.2 - Prob. 11E Ch. 12.2 - Prob. 12E Ch. 12.2 - Prob. 13E Ch. 12.2 - Prob. 14E Ch. 12.2 - Prob. 15E Ch. 12.2 - Prob. 16E Ch. 12.2 - Prob. 17E Ch. 12.2 - Prob. 18E Ch. 12.2 - Prob. 19E Ch. 12.2 - Prob. 20E Ch. 12.2 - Prob. 21E Ch. 12.2 - Prob. 22E Ch. 12.2 - Prob. 23E Ch. 12.2 - Prob. 24E Ch. 12.2 - Prob. 25E Ch. 12.2 - Prob. 26E Ch. 12.2 - An experiment consists of selecting a point at...Ch. 12.2 - Prob. 28E Ch. 12.2 - Prob. 29E Ch. 12.2 - Prob. 30E Ch. 12.2 - Prob. 31E Ch. 12.2 - Prob. 32E Ch. 12.2 - Prob. 33E Ch. 12.2 - Prob. 34E Ch. 12.2 - Prob. 35E Ch. 12.2 - A random variable X has a cumulative distribution...Ch. 12.2 - Prob. 37E Ch. 12.2 - Prob. 38E Ch. 12.3 - Prob. 1CYU Ch. 12.3 - Prob. 2CYU Ch. 12.3 - Prob. 1E Ch. 12.3 - Prob. 2E Ch. 12.3 - Prob. 3E Ch. 12.3 - Prob. 4E Ch. 12.3 - Prob. 5E Ch. 12.3 - Prob. 6E Ch. 12.3 - Prob. 7E Ch. 12.3 - Prob. 8E Ch. 12.3 - Prob. 9E Ch. 12.3 - Prob. 10E Ch. 12.3 - Prob. 11E Ch. 12.3 - Prob. 12E Ch. 12.3 - Expected Reading Time The amount oftime (in...Ch. 12.3 - Prob. 14E Ch. 12.3 - Prob. 15E Ch. 12.3 - Prob. 16E Ch. 12.3 - Prob. 17E Ch. 12.3 - Prob. 18E Ch. 12.3 - If X is a random variable with density function...Ch. 12.3 - Prob. 20E Ch. 12.3 - Prob. 21E Ch. 12.3 - Prob. 22E Ch. 12.3 - Prob. 23E Ch. 12.3 - Prob. 24E Ch. 12.3 - Prob. 25E Ch. 12.3 - Prob. 26E Ch. 12.4 - The emergency flasher on an automobile is...Ch. 12.4 - Prob. 2CYU Ch. 12.4 - Prob. 1E Ch. 12.4 - Prob. 2E Ch. 12.4 - Prob. 3E Ch. 12.4 - Prob. 4E Ch. 12.4 - Prob. 5E Ch. 12.4 - In a large factory there is an average of two...Ch. 12.4 - Prob. 7E Ch. 12.4 - Prob. 8E Ch. 12.4 - During a certain part of the day, the time between...Ch. 12.4 - During a certain part of the day, the time between...Ch. 12.4 - Prob. 11E Ch. 12.4 - Prob. 12E Ch. 12.4 - Reliability of Electronic Components Suppose that...Ch. 12.4 - Prob. 14E Ch. 12.4 - Prob. 15E Ch. 12.4 - Find the expected values and the standard...Ch. 12.4 - Prob. 17E Ch. 12.4 - Find the expected values and the standard...Ch. 12.4 - Prob. 19E Ch. 12.4 - Prob. 20E Ch. 12.4 - Prob. 21E Ch. 12.4 - Prob. 22E Ch. 12.4 - Prob. 23E Ch. 12.4 - Prob. 24E Ch. 12.4 - Prob. 25E Ch. 12.4 - Normal Distribution and Life of a Tire Suppose...Ch. 12.4 - Amount of Milk in a Container If the amount of...Ch. 12.4 - Breaking weight Theamount of weight required to...Ch. 12.4 - Time of a commute A student with an eight oclock...Ch. 12.4 - Prob. 30E Ch. 12.4 - Diameter of a Bolt A certain type of bolt must fit...Ch. 12.4 - Prob. 32E Ch. 12.4 - Prob. 33E Ch. 12.4 - Prob. 34E Ch. 12.4 - Prob. 35E Ch. 12.4 - Prob. 36E Ch. 12.4 - Prob. 37E Ch. 12.5 - A public health officer is tracking down the...Ch. 12.5 - Suppose that a random variable X has a Poisson...Ch. 12.5 - Prob. 2E Ch. 12.5 - Prob. 3E Ch. 12.5 - Prob. 4E Ch. 12.5 - Number of Insurance Claims The monthly number of...Ch. 12.5 - Waiting Time in an Emergency Room On a typical...Ch. 12.5 - Prob. 7E Ch. 12.5 - Number of Cars at a Tollgate During a certain part...Ch. 12.5 - Poisson Distribution in a Mixing Problem A bakery...Ch. 12.5 - Prob. 10E Ch. 12.5 - Prob. 11E Ch. 12.5 - Quality Control The quality-control department at...Ch. 12.5 - Two Competing Companies In a certain town, there...Ch. 12.5 - Prob. 14E Ch. 12.5 - Prob. 15E Ch. 12.5 - Prob. 16E Ch. 12.5 - Prob. 17E Ch. 12.5 - Prob. 18E Ch. 12.5 - Prob. 19E Ch. 12.5 - Prob. 20E Ch. 12.5 - Prob. 21E Ch. 12.5 - Prob. 22E Ch. 12.5 - Prob. 23E Ch. 12.5 - Prob. 24E Ch. 12.5 - Prob. 25E Ch. 12.5 - The number of accidents occurring each month at a...Ch. 12 - What is probability table?Ch. 12 - Prob. 2FCCE Ch. 12 - Prob. 3FCCE Ch. 12 - Prob. 4FCCE Ch. 12 - Prob. 5FCCE Ch. 12 - Prob. 6FCCE Ch. 12 - Prob. 7FCCE Ch. 12 - Prob. 8FCCE Ch. 12 - Prob. 9FCCE Ch. 12 - Give two ways to compute the variance of a...Ch. 12 - Prob. 11FCCE Ch. 12 - Prob. 12FCCE Ch. 12 - Prob. 13FCCE Ch. 12 - Prob. 14FCCE Ch. 12 - How is an integral involving a normal density...Ch. 12 - Prob. 16FCCE Ch. 12 - Prob. 17FCCE Ch. 12 - Let X be a continuous random variable on 0x2, with...Ch. 12 - Prob. 2RE Ch. 12 - Prob. 3RE Ch. 12 - Prob. 4RE Ch. 12 - Prob. 5RE Ch. 12 - Prob. 6RE Ch. 12 - Prob. 7RE Ch. 12 - Prob. 8RE Ch. 12 - Probability of Gasoline Sales A certain gas...Ch. 12 - Prob. 10RE Ch. 12 - Prob. 11RE Ch. 12 - Prob. 12RE Ch. 12 - Prob. 13RE Ch. 12 - Prob. 14RE Ch. 12 - Prob. 15RE Ch. 12 - Prob. 16RE Ch. 12 - Prob. 17RE Ch. 12 - Deciding on a Service Contract The condenser motor...Ch. 12 - Prob. 19RE Ch. 12 - Prob. 20RE Ch. 12 - Prob. 21RE Ch. 12 - Prob. 22RE Ch. 12 - Prob. 23RE Ch. 12 - Prob. 24RE Ch. 12 - Prob. 25RE Ch. 12 - Prob. 26RE Ch. 12 - Area under the Normal Curve It is useful in some...Ch. 12 - Prob. 28RE Ch. 12 - Prob. 29RE Ch. 12 - Prob. 30RE Ch. 12 - Prob. 31RE Ch. 12 - Prob. 32RE Ch. 12 - Prob. 33RE Ch. 12 - Rolling Dice A pair of dice is rolled until a 7 or...Ch. 12 - Rolling Dice A pair of dice is rolled until a 7 or...Ch. 12 - Rolling Dice A pair of dice is rolled until a 7 or...

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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 ) .