Explanation Given information: A function is given by p ( x ) = 3 x − 4 on the interval [ 1 , ∞ ) . Formula used: A function p ( x ) will be a probability density function of a random variable X , if it satisfies the following condition. 1). p ( x ) ≥ 0 for all x ∈ R 2). ∫ − ∞ ∞ p ( x ) d x = 1 3). P ( a ≤ X ≤ b ) = ∫ a b p ( x ) d x = F ( b ) − F ( a ) such that F is an antiderivative of f . The power rule of indefinite integrals. ∫ x n d x = x n n + 1 + C For a probability density function p ( x ) on ( − ∞ , ∞ ) , the mean μ of the random variable is given by μ = ∫ − ∞ ∞ x p ( x ) d x Calculation: Let us consider the given function. p ( x ) = 3 x − 4 Now p ( x ) should satisfy the condition ∫ 1 ∞ p ( x ) d x = 1 . ∫ − ∞ ∞ p ( x ) d x = ∫ 1 ∞ 3 x − 4 d x = lim A → ∞ ∫ 1 A 3 x − 4 d x = lim A → ∞ 3 [ x − 3

Loose-leaf Version For Calculus: Early Transcendentals

4th Edition

ISBN: 9781319055912

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Question

Chapter 8.1, Problem 9E

To determine

To find:

Whether p(x) is a probability density function on [1,∞) and calculate the mean.

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Chapter 8.1, Problem 8E

Chapter 8.1, Problem 10E

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Chapter 8 Solutions

Loose-leaf Version For Calculus: Early Transcendentals

Ch. 8.1 - Prob. 1PQ Ch. 8.1 - Prob. 2PQ Ch. 8.1 - Prob. 3PQ Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E

Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E Ch. 8.1 - Prob. 11E Ch. 8.1 - Prob. 12E Ch. 8.1 - Prob. 13E Ch. 8.1 - Prob. 14E Ch. 8.1 - Prob. 15E Ch. 8.1 - Prob. 16E Ch. 8.1 - Prob. 17E Ch. 8.1 - Prob. 18E Ch. 8.1 - Prob. 19E Ch. 8.1 - Prob. 20E Ch. 8.1 - Prob. 21E Ch. 8.1 - Prob. 22E Ch. 8.1 - Prob. 23E Ch. 8.1 - Prob. 24E Ch. 8.1 - Prob. 25E Ch. 8.1 - Prob. 26E Ch. 8.1 - Prob. 27E Ch. 8.1 - Prob. 28E Ch. 8.1 - Prob. 29E Ch. 8.1 - Prob. 30E Ch. 8.1 - Prob. 31E Ch. 8.1 - Prob. 32E Ch. 8.2 - Prob. 1PQ Ch. 8.2 - Prob. 2PQ Ch. 8.2 - Prob. 3PQ Ch. 8.2 - Prob. 4PQ Ch. 8.2 - Prob. 5PQ Ch. 8.2 - Prob. 1E Ch. 8.2 - Prob. 2E Ch. 8.2 - Prob. 3E Ch. 8.2 - Prob. 4E Ch. 8.2 - Prob. 5E Ch. 8.2 - Prob. 6E Ch. 8.2 - Prob. 7E Ch. 8.2 - Prob. 8E Ch. 8.2 - Prob. 9E Ch. 8.2 - Prob. 10E Ch. 8.2 - Prob. 11E Ch. 8.2 - Prob. 12E Ch. 8.2 - Prob. 13E Ch. 8.2 - Prob. 14E Ch. 8.2 - Prob. 15E Ch. 8.2 - Prob. 16E Ch. 8.2 - Prob. 17E Ch. 8.2 - Prob. 18E Ch. 8.2 - Prob. 19E Ch. 8.2 - Prob. 20E Ch. 8.2 - Prob. 21E Ch. 8.2 - Prob. 22E Ch. 8.2 - Prob. 23E Ch. 8.2 - Prob. 24E Ch. 8.2 - Prob. 25E Ch. 8.2 - Prob. 26E Ch. 8.2 - Prob. 27E Ch. 8.2 - Prob. 28E Ch. 8.2 - Prob. 29E Ch. 8.2 - Prob. 30E Ch. 8.2 - Prob. 31E Ch. 8.2 - Prob. 32E Ch. 8.2 - Prob. 33E Ch. 8.2 - Prob. 34E Ch. 8.2 - Prob. 35E Ch. 8.2 - Prob. 36E Ch. 8.2 - Prob. 37E Ch. 8.2 - Prob. 38E Ch. 8.2 - Prob. 39E Ch. 8.2 - Prob. 40E Ch. 8.2 - Prob. 41E Ch. 8.2 - Prob. 42E Ch. 8.2 - Prob. 43E Ch. 8.2 - Prob. 44E Ch. 8.2 - Prob. 45E Ch. 8.2 - Prob. 46E Ch. 8.2 - Prob. 47E Ch. 8.2 - Prob. 48E Ch. 8.2 - Prob. 49E Ch. 8.2 - Prob. 50E Ch. 8.2 - Prob. 51E Ch. 8.2 - Prob. 52E Ch. 8.2 - Prob. 53E Ch. 8.2 - Prob. 54E Ch. 8.2 - Prob. 55E Ch. 8.2 - Prob. 56E Ch. 8.2 - Prob. 57E Ch. 8.2 - Prob. 58E Ch. 8.2 - Prob. 59E Ch. 8.2 - Prob. 60E Ch. 8.2 - Prob. 61E Ch. 8.2 - Prob. 62E Ch. 8.2 - Prob. 63E Ch. 8.2 - Prob. 64E Ch. 8.2 - Prob. 65E Ch. 8.3 - Prob. 1PQ Ch. 8.3 - Prob. 2PQ Ch. 8.3 - Prob. 3PQ Ch. 8.3 - Prob. 4PQ Ch. 8.3 - Prob. 5PQ Ch. 8.3 - Prob. 1E Ch. 8.3 - Prob. 2E Ch. 8.3 - Prob. 3E Ch. 8.3 - Prob. 4E Ch. 8.3 - Prob. 5E Ch. 8.3 - Prob. 6E Ch. 8.3 - Prob. 7E Ch. 8.3 - Prob. 8E Ch. 8.3 - Prob. 9E Ch. 8.3 - Prob. 10E Ch. 8.3 - Prob. 11E Ch. 8.3 - Prob. 12E Ch. 8.3 - Prob. 13E Ch. 8.3 - Prob. 14E Ch. 8.3 - Prob. 15E Ch. 8.3 - Prob. 16E Ch. 8.3 - Prob. 17E Ch. 8.3 - Prob. 18E Ch. 8.3 - Prob. 19E Ch. 8.3 - Prob. 20E Ch. 8.3 - Prob. 21E Ch. 8.3 - Prob. 22E Ch. 8.3 - Prob. 23E Ch. 8.3 - Prob. 24E Ch. 8.3 - Prob. 25E Ch. 8.3 - Prob. 26E Ch. 8.3 - Prob. 27E Ch. 8.3 - Prob. 28E Ch. 8.3 - Prob. 29E Ch. 8.3 - Prob. 30E Ch. 8.4 - Prob. 1PQ Ch. 8.4 - Prob. 2PQ Ch. 8.4 - Prob. 3PQ Ch. 8.4 - Prob. 4PQ Ch. 8.4 - Prob. 5PQ Ch. 8.4 - Prob. 6PQ Ch. 8.4 - Prob. 1E Ch. 8.4 - Prob. 2E Ch. 8.4 - Prob. 3E Ch. 8.4 - Prob. 4E Ch. 8.4 - Prob. 5E Ch. 8.4 - Prob. 6E Ch. 8.4 - Prob. 7E Ch. 8.4 - Prob. 8E Ch. 8.4 - Prob. 9E Ch. 8.4 - Prob. 10E Ch. 8.4 - Prob. 11E Ch. 8.4 - Prob. 12E Ch. 8.4 - Prob. 13E Ch. 8.4 - Prob. 14E Ch. 8.4 - Prob. 15E Ch. 8.4 - Prob. 16E Ch. 8.4 - Prob. 17E Ch. 8.4 - Prob. 18E Ch. 8.4 - Prob. 19E Ch. 8.4 - Prob. 20E Ch. 8.4 - Prob. 21E Ch. 8.4 - Prob. 22E Ch. 8.4 - Prob. 23E Ch. 8.4 - Prob. 24E Ch. 8.4 - Prob. 25E Ch. 8.4 - Prob. 26E Ch. 8.4 - Prob. 27E Ch. 8.4 - Prob. 28E Ch. 8.4 - Prob. 29E Ch. 8.4 - Prob. 30E Ch. 8.4 - Prob. 31E Ch. 8.4 - Prob. 32E Ch. 8.4 - Prob. 33E Ch. 8.4 - Prob. 34E Ch. 8.4 - Prob. 35E Ch. 8.4 - Prob. 36E Ch. 8.4 - Prob. 37E Ch. 8.4 - Prob. 38E Ch. 8.4 - Prob. 39E Ch. 8.4 - Prob. 40E Ch. 8.4 - Prob. 41E Ch. 8.4 - Prob. 42E Ch. 8.4 - Prob. 43E Ch. 8.4 - Prob. 44E Ch. 8.4 - Prob. 45E Ch. 8.4 - Prob. 46E Ch. 8.4 - Prob. 47E Ch. 8.4 - Prob. 48E Ch. 8.4 - Prob. 49E Ch. 8.4 - Prob. 50E Ch. 8.4 - Prob. 51E Ch. 8 - Prob. 1CRE Ch. 8 - Prob. 2CRE Ch. 8 - Prob. 3CRE Ch. 8 - Prob. 4CRE Ch. 8 - Prob. 5CRE Ch. 8 - Prob. 6CRE Ch. 8 - Prob. 7CRE Ch. 8 - Prob. 8CRE Ch. 8 - Prob. 9CRE Ch. 8 - Prob. 10CRE Ch. 8 - Prob. 11CRE Ch. 8 - Prob. 12CRE Ch. 8 - Prob. 13CRE Ch. 8 - Prob. 14CRE Ch. 8 - Prob. 15CRE Ch. 8 - Prob. 16CRE Ch. 8 - Prob. 17CRE Ch. 8 - Prob. 18CRE Ch. 8 - Prob. 19CRE Ch. 8 - Prob. 20CRE Ch. 8 - Prob. 21CRE Ch. 8 - Prob. 22CRE Ch. 8 - Prob. 23CRE Ch. 8 - Prob. 24CRE Ch. 8 - Prob. 25CRE Ch. 8 - Prob. 26CRE Ch. 8 - Prob. 27CRE Ch. 8 - Prob. 28CRE

Knowledge Booster

Whether p ( x ) is a probability density function on [ 1 , ∞ ) and calculate the mean.

Solution Summary: The author explains that p(x) is a probability density function on X if it satisfies the following condition.

To find:

Whether p(x) is a probability density function on [1,∞) and calculate the mean.

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Chapter 8 Solutions

Whether p ( x ) is a probability density function on [ 1 , ∞ ) and calculate the mean.

Solution Summary: The author explains that p(x) is a probability density function on X if it satisfies the following condition.

To find: Whether p(x) is a probability density function on [1,∞) and calculate the mean.

Want to see the full answer?

Chapter 8 Solutions

To find:

Whether p(x) is a probability density function on [1,∞) and calculate the mean.