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
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 11, Problem 9RE
To determine
To find: The probability density function f and the cumulative distribution function F for the continuous random variable X which is uniformly distributed on
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
7. If a random variable has the probability density function
-1≤x≤3
otherwise
f(x)=k(x²-1)
=0
1. If the joint probability distribution of X and Y is given by
f(x,y)=**Y, forx=0,1,2,3; y=0,1,2,
30
find
a. P(X1)
b. P(X+Y=4)
3. Suppose it is known from large amounts of historical data that X, the number of cars that arrive at a
specific intersection during a 20-second time period, is characterized by the following discrete probability
function:
6x
f(x) = e-6, for x = 0,1,2, ...
a) Find the probability that in a specific 20-second time period, more than 8 cars arrive at the
intersection.
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. 2MPCh. 11.1 - Prob. 3MPCh. 11.1 - Prob. 4MPCh. 11.1 - Prob. 5MPCh. 11.1 - Prob. 6MPCh. 11.1 - Prob. 1EDCh. 11.1 - Prob. 2EDCh. 11.1 - Prob. 1ECh. 11.1 - Prob. 2E
Ch. 11.1 - Prob. 3ECh. 11.1 - Prob. 4ECh. 11.1 - Prob. 5ECh. 11.1 - Prob. 6ECh. 11.1 - Prob. 7ECh. 11.1 - Prob. 8ECh. 11.1 - In Problems 928, find the value of each improper...Ch. 11.1 - In Problems 928, find the value of each improper...Ch. 11.1 - In Problems 928, find the value of each improper...Ch. 11.1 - In Problems 928, find the value of each improper...Ch. 11.1 - Prob. 13ECh. 11.1 - In Problems 928, find the value of each improper...Ch. 11.1 - In Problems 928, find the value of each improper...Ch. 11.1 - In Problems 928, find the value of each improper...Ch. 11.1 - In Problems 928, find the value of each improper...Ch. 11.1 - Prob. 18ECh. 11.1 - Prob. 19ECh. 11.1 - In Problems 928, find the value of each improper...Ch. 11.1 - In Problems 928, find the value of each improper...Ch. 11.1 - In Problems 928, find the value of each improper...Ch. 11.1 - In Problems 928, find the value of each improper...Ch. 11.1 - Prob. 24ECh. 11.1 - Prob. 25ECh. 11.1 - In Problems 928, find the value of each improper...Ch. 11.1 - In Problems 928, find the value of each improper...Ch. 11.1 - Prob. 28ECh. 11.1 - Prob. 29ECh. 11.1 - In Problems 2934, graph y = f(x) and find the...Ch. 11.1 - Prob. 31ECh. 11.1 - Prob. 32ECh. 11.1 - Prob. 33ECh. 11.1 - Prob. 34ECh. 11.1 - Prob. 35ECh. 11.1 - In Problems 3538, discuss the validity of each...Ch. 11.1 - Prob. 37ECh. 11.1 - Prob. 38ECh. 11.1 - Prob. 39ECh. 11.1 - Prob. 40ECh. 11.1 - Prob. 41ECh. 11.1 - Prob. 42ECh. 11.1 - Prob. 43ECh. 11.1 - Prob. 44ECh. 11.1 - Prob. 45ECh. 11.1 - Prob. 46ECh. 11.1 - Prob. 47ECh. 11.1 - Prob. 48ECh. 11.1 - Prob. 49ECh. 11.1 - Prob. 50ECh. 11.1 - Prob. 51ECh. 11.1 - Prob. 52ECh. 11.1 - Prob. 53ECh. 11.1 - Prob. 54ECh. 11.1 - Prob. 55ECh. 11.1 - Prob. 56ECh. 11.1 - Prob. 57ECh. 11.1 - Prob. 58ECh. 11.1 - Prob. 59ECh. 11.1 - Prob. 60ECh. 11.1 - Prob. 61ECh. 11.1 - Prob. 62ECh. 11.1 - Prob. 63ECh. 11.1 - Prob. 64ECh. 11.1 - Prob. 65ECh. 11.1 - Prob. 66ECh. 11.1 - Prob. 67ECh. 11.1 - Prob. 68ECh. 11.1 - Prob. 69ECh. 11.1 - Prob. 70ECh. 11.1 - Prob. 71ECh. 11.1 - Prob. 72ECh. 11.2 - Let f(x)={6x6x2if0x10otherwise Graph f and verify...Ch. 11.2 - Prob. 2MPCh. 11.2 - Prob. 3MPCh. 11.2 - Prob. 4MPCh. 11.2 - Repeat Example 5 if the pharmacist wants the...Ch. 11.2 - For each of the following experiments, determine...Ch. 11.2 - Prob. 2EDCh. 11.2 - Prob. 1ECh. 11.2 - Prob. 2ECh. 11.2 - Prob. 3ECh. 11.2 - Prob. 4ECh. 11.2 - Prob. 5ECh. 11.2 - Prob. 6ECh. 11.2 - Prob. 7ECh. 11.2 - Prob. 8ECh. 11.2 - Prob. 9ECh. 11.2 - In Problems 9 and 10, graph f, and show that f...Ch. 11.2 - Prob. 11ECh. 11.2 - Prob. 12ECh. 11.2 - Prob. 13ECh. 11.2 - Prob. 14ECh. 11.2 - Use the function in Problem 9 to find the...Ch. 11.2 - Use the function in Problem 10 to find the...Ch. 11.2 - Use the function in Problem 9 to find the...Ch. 11.2 - Use the function in Problem 10 to find the...Ch. 11.2 - Prob. 19ECh. 11.2 - Prob. 20ECh. 11.2 - Prob. 21ECh. 11.2 - Prob. 22ECh. 11.2 - Prob. 23ECh. 11.2 - Use the cumulative distribution function from...Ch. 11.2 - In Problems 25 and 26, graph f, and show that f...Ch. 11.2 - In Problems 25 and 26, graph f, and show that f...Ch. 11.2 - Prob. 27ECh. 11.2 - Use the function in Problem 26 to find the...Ch. 11.2 - Prob. 29ECh. 11.2 - Prob. 30ECh. 11.2 - Prob. 31ECh. 11.2 - Prob. 32ECh. 11.2 - Prob. 33ECh. 11.2 - In Problems 3336, find the associated cumulative...Ch. 11.2 - Prob. 35ECh. 11.2 - Prob. 36ECh. 11.2 - Prob. 37ECh. 11.2 - Prob. 38ECh. 11.2 - Prob. 39ECh. 11.2 - Prob. 40ECh. 11.2 - Prob. 41ECh. 11.2 - Prob. 42ECh. 11.2 - Prob. 43ECh. 11.2 - Prob. 44ECh. 11.2 - Prob. 45ECh. 11.2 - Prob. 46ECh. 11.2 - Prob. 47ECh. 11.2 - Prob. 48ECh. 11.2 - Prob. 49ECh. 11.2 - Prob. 50ECh. 11.2 - Prob. 51ECh. 11.2 - Prob. 52ECh. 11.2 - Prob. 53ECh. 11.2 - Prob. 54ECh. 11.2 - In Problems 53 and 58, find the associated...Ch. 11.2 - In Problems 53 and 58, find the associated...Ch. 11.2 - Prob. 57ECh. 11.2 - In Problems 53 and 58, find the associated...Ch. 11.2 - Demand. The weekly demand for hamburger (in...Ch. 11.2 - Prob. 60ECh. 11.2 - Prob. 61ECh. 11.2 - Prob. 62ECh. 11.2 - Prob. 63ECh. 11.2 - Shelf life. Repeat Problem 63 if...Ch. 11.2 - Prob. 65ECh. 11.2 - Prob. 66ECh. 11.3 - Find the expected value (mean), variance, and...Ch. 11.3 - Repeat Example 2 if the probability density...Ch. 11.3 - Prob. 3MPCh. 11.3 - Prob. 4MPCh. 11.3 - Prob. 5MPCh. 11.3 - Prob. 6MPCh. 11.3 - Prob. 1EDCh. 11.3 - Prob. 2EDCh. 11.3 - In Problems 16, find the mean, variance, and...Ch. 11.3 - In Problems 16, find the mean, variance, and...Ch. 11.3 - In Problems 16, find the mean, variance, and...Ch. 11.3 - Prob. 4ECh. 11.3 - Prob. 5ECh. 11.3 - Prob. 6ECh. 11.3 - In Problems 712, find the median....Ch. 11.3 - Prob. 8ECh. 11.3 - Prob. 9ECh. 11.3 - In Problems 712, find the median....Ch. 11.3 - In Problems 712, find the median....Ch. 11.3 - Prob. 12ECh. 11.3 - Prob. 13ECh. 11.3 - Prob. 14ECh. 11.3 - Prob. 15ECh. 11.3 - Prob. 16ECh. 11.3 - In Problems 1720, find the mean, variance, and...Ch. 11.3 - Prob. 18ECh. 11.3 - In Problems 1720, find the mean, variance, and...Ch. 11.3 - In Problems 1720, find the mean, variance, and...Ch. 11.3 - In Problems 21 and 22, use a graphing calculator...Ch. 11.3 - Prob. 22ECh. 11.3 - Prob. 23ECh. 11.3 - Prob. 24ECh. 11.3 - Prob. 25ECh. 11.3 - Prob. 26ECh. 11.3 - Prob. 27ECh. 11.3 - Prob. 28ECh. 11.3 - Prob. 29ECh. 11.3 - Prob. 30ECh. 11.3 - Prob. 31ECh. 11.3 - Prob. 32ECh. 11.3 - Prob. 33ECh. 11.3 - Prob. 34ECh. 11.3 - Prob. 35ECh. 11.3 - Prob. 36ECh. 11.3 - Prob. 37ECh. 11.3 - Prob. 38ECh. 11.3 - Prob. 39ECh. 11.3 - Prob. 40ECh. 11.3 - Prob. 41ECh. 11.3 - Prob. 42ECh. 11.3 - Prob. 43ECh. 11.3 - Prob. 44ECh. 11.3 - Prob. 45ECh. 11.3 - Electricity consumption. The daily consumption of...Ch. 11.3 - Prob. 47ECh. 11.3 - Product life. The life expectancy (in years) of an...Ch. 11.3 - Prob. 49ECh. 11.3 - Prob. 50ECh. 11.3 - Prob. 51ECh. 11.3 - Prob. 52ECh. 11.3 - Prob. 53ECh. 11.3 - Prob. 54ECh. 11.3 - Learning. The number of hours it takes a...Ch. 11.3 - Prob. 56ECh. 11.4 - Use the probability density function given in...Ch. 11.4 - Prob. 2MPCh. 11.4 - Prob. 3MPCh. 11.4 - In Example 4, what percentage of the lightbulbs...Ch. 11.4 - Prob. 5MPCh. 11.4 - Prob. 2EDCh. 11.4 - Prob. 1ECh. 11.4 - Prob. 2ECh. 11.4 - Prob. 3ECh. 11.4 - Prob. 4ECh. 11.4 - Prob. 5ECh. 11.4 - Prob. 6ECh. 11.4 - Prob. 7ECh. 11.4 - Prob. 8ECh. 11.4 - Prob. 9ECh. 11.4 - Prob. 10ECh. 11.4 - In Problems 914, use Table 2 in Appendix C to find...Ch. 11.4 - Prob. 12ECh. 11.4 - Prob. 13ECh. 11.4 - In Problems 914, use Table 2 in Appendix C to find...Ch. 11.4 - Prob. 15ECh. 11.4 - Prob. 16ECh. 11.4 - Prob. 17ECh. 11.4 - Prob. 18ECh. 11.4 - Prob. 19ECh. 11.4 - Prob. 20ECh. 11.4 - Prob. 21ECh. 11.4 - Prob. 22ECh. 11.4 - Prob. 23ECh. 11.4 - Prob. 24ECh. 11.4 - Prob. 25ECh. 11.4 - Prob. 26ECh. 11.4 - Prob. 27ECh. 11.4 - Prob. 28ECh. 11.4 - Prob. 29ECh. 11.4 - Prob. 30ECh. 11.4 - Prob. 31ECh. 11.4 - Prob. 32ECh. 11.4 - Prob. 33ECh. 11.4 - Prob. 34ECh. 11.4 - Prob. 35ECh. 11.4 - Prob. 36ECh. 11.4 - Prob. 37ECh. 11.4 - Prob. 38ECh. 11.4 - Prob. 39ECh. 11.4 - Prob. 40ECh. 11.4 - Prob. 41ECh. 11.4 - Prob. 42ECh. 11.4 - Prob. 43ECh. 11.4 - Prob. 44ECh. 11.4 - Prob. 45ECh. 11.4 - Prob. 46ECh. 11.4 - Prob. 47ECh. 11.4 - Prob. 48ECh. 11.4 - Prob. 49ECh. 11.4 - Prob. 50ECh. 11.4 - Prob. 51ECh. 11.4 - Prob. 52ECh. 11.4 - Prob. 53ECh. 11.4 - Prob. 54ECh. 11.4 - Prob. 55ECh. 11.4 - Prob. 56ECh. 11.4 - Problems 5558 refer to the normal random variable...Ch. 11.4 - Prob. 58ECh. 11.4 - Prob. 59ECh. 11.4 - Prob. 60ECh. 11.4 - Prob. 61ECh. 11.4 - Prob. 62ECh. 11.4 - Prob. 63ECh. 11.4 - Prob. 64ECh. 11.4 - Prob. 65ECh. 11.4 - Prob. 66ECh. 11.4 - Prob. 67ECh. 11.4 - Prob. 68ECh. 11.4 - Waiting time. The time (in minutes) applicants...Ch. 11.4 - Prob. 70ECh. 11.4 - Communications. The length of time for telephone...Ch. 11.4 - Prob. 72ECh. 11.4 - Prob. 73ECh. 11.4 - Prob. 74ECh. 11.4 - Prob. 75ECh. 11.4 - Prob. 76ECh. 11.4 - Prob. 77ECh. 11.4 - Prob. 78ECh. 11.4 - Prob. 79ECh. 11.4 - Prob. 80ECh. 11.4 - Prob. 81ECh. 11.4 - Prob. 82ECh. 11.4 - Prob. 83ECh. 11.4 - Prob. 84ECh. 11.4 - Prob. 85ECh. 11.4 - Prob. 86ECh. 11 - Prob. 1RECh. 11 - Prob. 2RECh. 11 - Prob. 3RECh. 11 - Prob. 4RECh. 11 - Prob. 5RECh. 11 - Prob. 6RECh. 11 - Prob. 7RECh. 11 - Prob. 8RECh. 11 - Prob. 9RECh. 11 - Prob. 10RECh. 11 - Prob. 11RECh. 11 - Prob. 12RECh. 11 - Prob. 13RECh. 11 - Prob. 14RECh. 11 - Prob. 15RECh. 11 - Prob. 16RECh. 11 - Prob. 17RECh. 11 - Prob. 18RECh. 11 - Prob. 19RECh. 11 - Prob. 20RECh. 11 - Prob. 21RECh. 11 - Prob. 22RECh. 11 - Prob. 23RECh. 11 - Prob. 24RECh. 11 - Prob. 25RECh. 11 - Prob. 26RECh. 11 - Prob. 27RECh. 11 - Prob. 28RECh. 11 - Prob. 29RECh. 11 - Prob. 30RECh. 11 - Prob. 31RECh. 11 - Prob. 32RECh. 11 - Prob. 33RECh. 11 - Prob. 34RECh. 11 - Prob. 35RECh. 11 - Prob. 36RECh. 11 - Prob. 37RECh. 11 - Prob. 38RECh. 11 - Prob. 39RECh. 11 - Credit applications. The percentage of...Ch. 11 - Prob. 41RECh. 11 - Prob. 42RECh. 11 - Prob. 43RECh. 11 - Medicine. The shelf life (in months) of a certain...Ch. 11 - Life expectancy. The life expectancy (in months)...Ch. 11 - Prob. 46RECh. 11 - Prob. 47RECh. 11 - Prob. 48RE
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.Similar questions
- 9. If X is a continuous random variable with probability density function given by f(x) = x(x-x¹) =0 0≤x≤1 otherwisearrow_forward1. The cumulative probability function of a discrete random variable X is given in the following table: 1 2 3 f(x) 1/8 3/8 3/8 1/8 a. Find the distribution function F(x) for the random variable X. b. Graph this distribution function.arrow_forward2. In commuting to work, a professor must first get on a bus near her house and then transfer to a second bus. The total waiting time Y in minutes can be shown to have the following PDF 0sy<5 25 f(Y = y) = {2 1 5 25 5sys 10 otherwise a. What is the probability that total waiting time is at most 8 min? b. What is the probability that total waiting time is either less than 2 min or more than 6 min? c. What is the expected total waiting time for the professor? d. Determine the standard deviation in the total waiting time.arrow_forward
- 5. If X and Y have the joint probability distribution f(x, y)=1/4, for x=-1and y=-1,x=-1 and y=1,x=1 and y=-1,x=1 and y=1, X and Y are disjoint O independent O dependent exhaustivearrow_forwardFor what values of k canf(x) = (1 − k)kx serve as the values of the probability distribution of arandom variable with the countably infinite range x =0, 1, 2, ...?arrow_forward2. If the random variable X has the probability density function f(x) = (1-x²), -1 < x < 1, 3 4 what is the variance of 15X + 2?arrow_forward
- 2. If the probability density function of a random variable is given by f(x) = kx 0≤x≤2 - 2k 2≤x≤4 = 6k-kx 4≤x≤6 Find (1) k, (H) P(1 ≤ x ≤ 3), and (iii) X.arrow_forward12. Suppose that it is known from large amounts of historical data that X, the number of cars that arrive at a specific intersection during a 20-second time period, is characterized by the following discrete probability function: P(X = x) = e-6, for x = 0,1, 2, . Find the probability that in a specific 20-second time period, only two cars arrive at the intersection.arrow_forward3. Determine the value c so that each of the following functions can serve as probability distributions of the discrete random variable X: a. f(x) = c(x² +4) for x = 0,1, 2, 3; 3 b. f(x)%3Dс for x= 0,1, 2 3-xarrow_forward
- solve for the mean and variance plsarrow_forward1. An office has four copying machines, and the random variable X measures how many of them are in use at a particular moment in time. Suppose that P(X = 0) = 0.08, P(X= 1) = 0.11, P(X= 2) = 0.27, and P(X = 3) = 0.33. What is P(X = 4)? Draw a line graph of the probability mass function. Construct and plot the cumulative distribution function. а. b. с.arrow_forward9) The effectiveness of solar-energy heating units depends on the amount of radiation available from the sun. During a typical October, daily total solar radiation in Tampa, Florida, approximately follows the following probability density function (units are in hundreds of calories): 3 f (x) ={32 (x- 2)(6-x) for2arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
Recommended textbooks for you
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning
Calculus: Early Transcendentals
Calculus
ISBN:9781285741550
Author:James Stewart
Publisher:Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:9780134438986
Author:Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:9780134763644
Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:9781319050740
Author:Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:9781337552516
Author:Ron Larson, Bruce H. Edwards
Publisher:Cengage Learning
Continuous Probability Distributions - Basic Introduction; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=QxqxdQ_g2uw;License: Standard YouTube License, CC-BY
Probability Density Function (p.d.f.) Finding k (Part 1) | ExamSolutions; Author: ExamSolutions;https://www.youtube.com/watch?v=RsuS2ehsTDM;License: Standard YouTube License, CC-BY
Find the value of k so that the Function is a Probability Density Function; Author: The Math Sorcerer;https://www.youtube.com/watch?v=QqoCZWrVnbA;License: Standard Youtube License