
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
expand_more
expand_more
format_list_bulleted
Question
Can you help me with this? I don’t know why but I keep getting the Variance for part A and B wrong
![Consider a small ferry that can accommodate cars and buses. The toll for cars is $3, and the toll for buses is $10. Let \( X \) and \( Y \) denote the number of cars and buses, respectively, carried on a single trip. The joint probability mass function (pmf) of \( X \) and \( Y \) is given in the table below.
| \( p(x, y) \) | \( y = 0 \) | \( y = 1 \) | \( y = 2 \) |
|---------------|------------|------------|------------|
| \( x = 0 \) | 0.100 | 0.060 | 0.040 |
| \( x = 1 \) | 0.050 | 0.030 | 0.020 |
| \( x = 2 \) | 0.125 | 0.075 | 0.050 |
| \( x = 3 \) | 0.025 | 0.015 | 0.010 |
| \( x = 4 \) | 0.025 | 0.015 | 0.010 |
| \( x = 5 \) | 0.150 | 0.090 | 0.060 |
It is readily verified that \( X \) and \( Y \) are independent.
**(a) Compute the expected value, variance, and standard deviation of the total number of vehicles on a single trip.** (Round your standard deviation to two decimal places.)
- **Expected value:** 3.35 vehicles
- **Variance:** 11.75
- **Standard deviation:** 2.06 vehicles
**(b) If each car is charged $3 and each bus $10, compute the expected value (in $), variance, and standard deviation (in $) of the revenue resulting from a single trip.** (Round your standard deviation to two decimal places.)
- **Expected value:** $14.95
- **Variance:** [Incorrect value entered]
- **Standard deviation:** [Incorrect value entered]](https://content.bartleby.com/qna-images/question/78de2526-b393-406f-b144-213aa508c7e8/9ce0c0ee-c4e1-44aa-aae3-875f8b9b597b/ej7l3d_thumbnail.jpeg)
Transcribed Image Text:Consider a small ferry that can accommodate cars and buses. The toll for cars is $3, and the toll for buses is $10. Let \( X \) and \( Y \) denote the number of cars and buses, respectively, carried on a single trip. The joint probability mass function (pmf) of \( X \) and \( Y \) is given in the table below.
| \( p(x, y) \) | \( y = 0 \) | \( y = 1 \) | \( y = 2 \) |
|---------------|------------|------------|------------|
| \( x = 0 \) | 0.100 | 0.060 | 0.040 |
| \( x = 1 \) | 0.050 | 0.030 | 0.020 |
| \( x = 2 \) | 0.125 | 0.075 | 0.050 |
| \( x = 3 \) | 0.025 | 0.015 | 0.010 |
| \( x = 4 \) | 0.025 | 0.015 | 0.010 |
| \( x = 5 \) | 0.150 | 0.090 | 0.060 |
It is readily verified that \( X \) and \( Y \) are independent.
**(a) Compute the expected value, variance, and standard deviation of the total number of vehicles on a single trip.** (Round your standard deviation to two decimal places.)
- **Expected value:** 3.35 vehicles
- **Variance:** 11.75
- **Standard deviation:** 2.06 vehicles
**(b) If each car is charged $3 and each bus $10, compute the expected value (in $), variance, and standard deviation (in $) of the revenue resulting from a single trip.** (Round your standard deviation to two decimal places.)
- **Expected value:** $14.95
- **Variance:** [Incorrect value entered]
- **Standard deviation:** [Incorrect value entered]
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution
Trending nowThis is a popular solution!
Step by stepSolved in 2 steps with 8 images

Knowledge Booster
Similar questions
- how do you find the variance of the mean squared errors from this tabearrow_forwardIf no data values are given but the mean and standard deviation is given how do I find the variance with just this information?arrow_forwardExplain what restriction of range is and what it tends to do to the magnitude of a correlation.arrow_forward
- Professor Hayashi has implemented a new book for his Fall 2013 statistics course. He wants to see if the new book has an effect on the exam average for Exam 3. He knows that the Exam 3 mean for all students who have taken his statistic course over the past 10 years is 77.2. He collects some data from a sample of 9 students and finds that the Exam 3 mean for his Fall 2013 statistics students is 81.7 with a variance of 32.49.Measure effect size using percentage of variancearrow_forwardExplain the t-test as it relates to its application to one samplesarrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman

MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc

Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning

Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning

Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON

The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman

Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman