Explanation Definition used: If f ( x ) is the probability density function for continuous random variable X , then The Mean, μ = E ( X ) = ∫ − ∞ ∞ x f ( x ) d x . The variance, V ( X ) = ∫ − ∞ ∞ ( x − μ ) 2 f ( x ) d x . The standard deviation, σ = V ( X ) . Calculation: The given function is f ( x ) = { 1 − 1 2 x if 0 ≤ x ≤ 2 0 othewise . Compute the mean of the function by using above definition. μ = ∫ − ∞ ∞ x f ( x ) d x = ∫ 0 2 x ( 1 − 1 2 x ) d x = [ x 2 2 ] 0 2 − 1 2 [ x 3 3 ] 0 2 = ( 4 2 − 0 ) − ( 8 6 − 0 ) = 2 3 Thus, the mean value of the function is 2 3

Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences -- Instant Access (Pearson+)

14th Edition

ISBN: 9780137554805

Author: Raymond Barnett, Michael Ziegler

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, Problem 5RE

To determine

To find: The mean, variance, and standard deviation of the function f(x)={1−12x if 0≤x≤20 othewise.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11, Problem 4RE

Chapter 11, Problem 6RE

Students have asked these similar questions

Tools Sign in Different masses and Indicated velocities Rotational inert > C C Chegg 39. The balls shown have different masses and speeds. Rank the following from greatest to least: 2.0 m/s 8.5 m/s 9.0 m/s 12.0 m/s 1.0 kg A 1.2 kg B 0.8 kg C 5.0 kg D C a. The momenta b. The impulses needed to stop the balls Solved 39. The balls shown have different masses and speeds. | Chegg.com Images may be subject to copyright. Learn More Share H Save Visit > quizlet.com%2FBoyE3qwOAUqXvw95Fgh5Rw.jpg&imgrefurl=https%3A%2F%2Fquizlet.com%2F529359992%2Fc. X

13. In 2000, two organizations conducted surveys to ascertain the public's opinion on banning gay men from serving in leadership roles in the Boy Scouts.• A Pew poll asked respondents whether they agreed with "the recent decision by the Supreme Court" that "the Boy Scouts of America have a constitutional right to block gay men from becoming troop leaders."A Los Angeles Times poll asked respondents whether they agreed with the following statement: "A Boy Scout leader should be removed from his duties as a troop leader if he is found out to be gay, even if he is considered by the Scout organization to be a model Boy Scout leader."One of these polls found 36% agreement; the other found 56% agreement. Which of the following statements is true?A) The Pew poll found 36% agreement, and the Los Angeles Times poll found 56% agreement.B) The Pew poll includes a leading question, while the Los Angeles Times poll uses neutral wording.C) The Los Angeles Times Poll includes a leading question, while…

A tank contains 60 kg of salt and 2000 L of water. Pure water enters a tank at the rate 8 L/min. The solution is mixed and drains from the tank at the rate 11 L/min. Let y be the number of kg of salt in the tank after t minutes. The differential equation for this situation would be: dy dt y(0) =

Chapter 11 Solutions

Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences -- Instant Access (Pearson+)

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 mean, variance, and standard deviation of the function f ( x ) = { 1 − 1 2 x if 0 ≤ x ≤ 2 0 othewise .

Solution Summary: The author calculates the mean, variance, and standard deviation of the function f(x) by using the above definition.

Concept explainers

Videos

To find: The mean, variance, and standard deviation of the function f(x)={1−12x if 0≤x≤20 othewise.

Want to see the full answer?

Chapter 11 Solutions