Homework Help is Here – Start Your Trial Now!
Math
Statistics
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. Suppose the joint distribution of X and Y is as given in the table below. P(x,y) 1. 2 0.025 0.015 0.010 1 0.050 0.030 0.020 0.060 0.075 0.050 0.150 0.090 0.060 4 0.100 0.060 0.040 5 0.050 0.030 0.085 Compute the expected revenue from a single trip. (Round your answer to two decimal places.) Need Help? Read It

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. Suppose the joint distribution of X and Y is as given in the table below. P(x,y) 1. 2 0.025 0.015 0.010 1 0.050 0.030 0.020 0.060 0.075 0.050 0.150 0.090 0.060 4 0.100 0.060 0.040 5 0.050 0.030 0.085 Compute the expected revenue from a single trip. (Round your answer to two decimal places.) Need Help? Read It

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question
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. Suppose the joint distribution of \( X \) and \( Y \) is as given in the table below. \[ \begin{array}{c|ccc} p(x,y) & y=0 & y=1 & y=2 \\ \hline x=0 & 0.025 & 0.015 & 0.010 \\ x=1 & 0.050 & 0.030 & 0.020 \\ x=2 & 0.060 & 0.075 & 0.050 \\ x=3 & 0.150 & 0.090 & 0.060 \\ x=4 & 0.100 & 0.060 & 0.040 \\ x=5 & 0.050 & 0.030 & 0.085 \\ \end{array} \] Compute the expected revenue from a single trip. (Round your answer to two decimal places.) \$ [ ] Need Help? - **Read It** (button) **Explanation:** This table represents the joint probability distribution of the number of cars \( X \) and the number of buses \( Y \) carried on a single trip by a ferry. Each cell in the table provides the probability of a specific combination of \( X \) cars and \( Y \) buses occurring. To compute the expected revenue from a single trip, multiply each possible revenue outcome by its corresponding probability and sum the results. The revenue for each combination is calculated by using the formula: \[ \text{Revenue} = 3X + 10Y \] where \( 3X \) is the total revenue from cars and \( 10Y \) is the total revenue from buses. Then, compute the expected value with: \[ \text{Expected Revenue} = \sum p(x,y) \times (3X + 10Y) \] Fill in the expected revenue calculation to get the final result.
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. Suppose the joint distribution of \( X \) and \( Y \) is as given in the table below. \[ \begin{array}{c|ccc} p(x,y) & y=0 & y=1 & y=2 \\ \hline x=0 & 0.025 & 0.015 & 0.010 \\ x=1 & 0.050 & 0.030 & 0.020 \\ x=2 & 0.060 & 0.075 & 0.050 \\ x=3 & 0.150 & 0.090 & 0.060 \\ x=4 & 0.100 & 0.060 & 0.040 \\ x=5 & 0.050 & 0.030 & 0.085 \\ \end{array} \] Compute the expected revenue from a single trip. (Round your answer to two decimal places.) \$ [ ] Need Help? - **Read It** (button) **Explanation:** This table represents the joint probability distribution of the number of cars \( X \) and the number of buses \( Y \) carried on a single trip by a ferry. Each cell in the table provides the probability of a specific combination of \( X \) cars and \( Y \) buses occurring. To compute the expected revenue from a single trip, multiply each possible revenue outcome by its corresponding probability and sum the results. The revenue for each combination is calculated by using the formula: \[ \text{Revenue} = 3X + 10Y \] where \( 3X \) is the total revenue from cars and \( 10Y \) is the total revenue from buses. Then, compute the expected value with: \[ \text{Expected Revenue} = \sum p(x,y) \times (3X + 10Y) \] Fill in the expected revenue calculation to get the final result.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Multivariate Distributions and Functions of Random Variables
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
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 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…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
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
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS