42. A large insurance agency provides services to a number of customers who have purchased both a homeowner's policy and an automobile policy. For each type of policy, a deductible amount must be specified. Let x denote the homeowner's deductible amount and y denote the automobile deductible amount for a customer who has both types of poli- cies. The joint mass function of x and y is as follows: y auto f(x, y) 250 500 200 .20 .10 .20 me 500 .05 .15 30
42. A large insurance agency provides services to a number of customers who have purchased both a homeowner's policy and an automobile policy. For each type of policy, a deductible amount must be specified. Let x denote the homeowner's deductible amount and y denote the automobile deductible amount for a customer who has both types of poli- cies. The joint mass function of x and y is as follows: y auto f(x, y) 250 500 200 .20 .10 .20 me 500 .05 .15 30
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
|
f(x,y) |
y |
|||
|
0 |
250 |
500 |
||
|
x |
200 |
0.20 |
0.10 |
0.20 |
|
500 |
0.05 |
0.15 |
0.30 |
The marginal mass
|
x |
200 |
500 |
|
f ( x ) |
0.5 |
0.5 |
The marginal mass function of y is
|
y |
0 |
250 |
500 |
|
f ( y ) |
0.25 |
0.25 |
0.5 |
Transcribed Image Text:Refer to Exercise 42. Compute the covariance between \( x \) and \( y \) and then the value of the population correlation coefficient. Do these two variables appear to be strongly related? Explain.
![**Title: Understanding Deductible Amounts in Insurance Policies**
**Introduction:**
A large insurance agency provides services to numerous customers who have purchased both a homeowner’s policy and an automobile policy. For each type of policy, a deductible amount must be specified. This section explores how these deductible amounts are determined and their implications.
**Notation:**
- Let \( x \) denote the homeowner’s deductible amount.
- Let \( y \) denote the automobile deductible amount.
**Joint Mass Function:**
For a customer who has both types of policies, the joint mass function of \( x \) and \( y \) is provided in the following table. This function helps us understand the probability distribution of various deductible scenarios:
\[
\begin{array}{c|ccc}
f(x, y) & y = 0 & y = 250 & y = 500 \\
\hline
x = 200 & 0.20 & 0.10 & 0.20 \\
x = 500 & 0.05 & 0.15 & 0.30 \\
\end{array}
\]
**Explanation of the Table:**
- The rows represent the different homeowner’s deductible amounts (\( x = 200 \) or \( x = 500 \)).
- The columns represent the different automobile deductible amounts (\( y = 0 \), \( y = 250 \), \( y = 500 \)).
- Each cell in the table denotes \( f(x, y) \), the joint probability of a customer having the specified combination of homeowner’s and automobile deductible amounts.
**Key Insights:**
- A customer with a homeowner’s deductible of $200 and an automobile deductible of $0 is quite likely, with a probability of 0.20.
- A higher homeowner’s deductible of $500, alongside an automobile deductible of $500, also appears to be common, with a probability of 0.30.
- These probabilities depict the risk distribution and can influence premium calculations for bundled insurance policies.
**Conclusion:**
Understanding this joint mass function is crucial for both insurance providers and customers. It aids in comprehending how deductible choices impact overall insurance costs and risk management strategies.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd627e045-d503-4693-9754-e0a854927fd5%2F0db4dd98-1d17-455d-ac01-5a3636eaabe4%2Fvwlm6v_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Deductible Amounts in Insurance Policies**
**Introduction:**
A large insurance agency provides services to numerous customers who have purchased both a homeowner’s policy and an automobile policy. For each type of policy, a deductible amount must be specified. This section explores how these deductible amounts are determined and their implications.
**Notation:**
- Let \( x \) denote the homeowner’s deductible amount.
- Let \( y \) denote the automobile deductible amount.
**Joint Mass Function:**
For a customer who has both types of policies, the joint mass function of \( x \) and \( y \) is provided in the following table. This function helps us understand the probability distribution of various deductible scenarios:
\[
\begin{array}{c|ccc}
f(x, y) & y = 0 & y = 250 & y = 500 \\
\hline
x = 200 & 0.20 & 0.10 & 0.20 \\
x = 500 & 0.05 & 0.15 & 0.30 \\
\end{array}
\]
**Explanation of the Table:**
- The rows represent the different homeowner’s deductible amounts (\( x = 200 \) or \( x = 500 \)).
- The columns represent the different automobile deductible amounts (\( y = 0 \), \( y = 250 \), \( y = 500 \)).
- Each cell in the table denotes \( f(x, y) \), the joint probability of a customer having the specified combination of homeowner’s and automobile deductible amounts.
**Key Insights:**
- A customer with a homeowner’s deductible of $200 and an automobile deductible of $0 is quite likely, with a probability of 0.20.
- A higher homeowner’s deductible of $500, alongside an automobile deductible of $500, also appears to be common, with a probability of 0.30.
- These probabilities depict the risk distribution and can influence premium calculations for bundled insurance policies.
**Conclusion:**
Understanding this joint mass function is crucial for both insurance providers and customers. It aids in comprehending how deductible choices impact overall insurance costs and risk management strategies.
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 now
This is a popular solution!
Step by step
Solved in 5 steps with 4 images
Recommended textbooks for you
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
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