Explanation Given: The quartile points for a probability density function are the values x 1 , x 2 , x 3 that divide the area under the graph of the function into four equal parts. Definition used: Cumulative distribution functions : If f is a probability function and F ( x ) = ∫ − ∞ x f ( t ) d t is the associated cumulative distribution function. Calculation: The given function is f ( x ) = { 3 ( 3 + x ) 2 if x ≥ 0 0 othewise . If x < 0 , then F ( x ) = 0 . In case of x ≥ 0 , the value of F ( x ) is as follows. F ( x ) = ∫ − ∞ x f ( t ) d t = ∫ − ∞ 0 0 d t + ∫ 0 x 3 ( 3 + t ) 2 d t = ( − 3 ( 3 + t ) ) 0 x = − 3 ( 3 + x ) − − 3 ( 3 + 0 ) On further simplification, F ( x ) = − 3 ( 3 + x ) + 1 = − 3 + 3 + x ( 3 + x ) = x 3 + x Thus, the value of F ( x ) is F ( x ) = { 0 , x < 0 x 3 + x , x ≥ 0

Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

14th Edition

ISBN: 9780134668574

Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen, Christopher J. Stocker

Publisher: PEARSON

See similar textbooks

Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could co…

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a…

Videos

Question

Chapter 11.3, Problem 39E

To determine

To find: The quartile points for the probability density function f(x)={3(3+x)2 if x≥00 othewise.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.3, Problem 38E

Chapter 11.3, Problem 40E

Students have asked these similar questions

Refer to page 110 for problems on optimization. Instructions: Given a loss function, analyze its critical points to identify minima and maxima. • Discuss the role of gradient descent in finding the optimal solution. . Compare convex and non-convex functions and their implications for optimization. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qo Hazb9tC440 AZF/view?usp=sharing]

Refer to page 140 for problems on infinite sets. Instructions: • Compare the cardinalities of given sets and classify them as finite, countable, or uncountable. • Prove or disprove the equivalence of two sets using bijections. • Discuss the implications of Cantor's theorem on real-world computation. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440 AZF/view?usp=sharing]

Refer to page 120 for problems on numerical computation. Instructions: • Analyze the sources of error in a given numerical method (e.g., round-off, truncation). • Compute the error bounds for approximating the solution of an equation. • Discuss strategies to minimize error in iterative methods like Newton-Raphson. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qo Hazb9tC440 AZF/view?usp=sharing]

Chapter 11 Solutions

Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

Ch. 11.1 - Evaluate the following, if it converges: 3dx(x1)2.Ch. 11.1 - Prob. 2MP Ch. 11.1 - Prob. 3MP Ch. 11.1 - Prob. 4MP Ch. 11.1 - Prob. 5MP Ch. 11.1 - Prob. 6MP Ch. 11.1 - Prob. 1ED Ch. 11.1 - Prob. 2ED Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The quartile points for the probability density function f ( x ) = { 3 ( 3 + x ) 2 if x ≥ 0 0 othewise .

Solution Summary: The author explains the quartile points for a probability density function.

Concept explainers

Videos

To find: The quartile points for the probability density function f(x)={3(3+x)2 if x≥00 othewise.

Want to see the full answer?

Chapter 11 Solutions