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 a. What proportion of customers have $500 de- ductible amounts for both types of policies? b. What proportion of customers have both de- ductible amounts less than $500? c. What is the marginal mass function of x? What is the marginal mass function of y?
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 a. What proportion of customers have $500 de- ductible amounts for both types of policies? b. What proportion of customers have both de- ductible amounts less than $500? c. What is the marginal mass function of x? What is the marginal mass function of y?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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I mostly need help with part C of 42 and question 45. This is ungraded homework.
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.
![**Educational Website Content:**
---
**Topic: Understanding Joint Mass Functions in Insurance**
**Introduction:**
A large insurance agency provides services to customers who have purchased both a homeowner's policy and an automobile policy. Each policy requires a specified deductible amount. Let \( x \) represent the homeowner’s deductible, and \( y \) represent the automobile deductible for customers with both policies.
**Joint Mass Function Explanation:**
The joint mass function \( f(x, y) \) is given as follows:
| \( x \) \\ \( y \) | 0 | 250 | 500 |
|---------------------|------|------|------|
| 200 | 0.20 | 0.10 | 0.20 |
| 500 | 0.05 | 0.15 | 0.30 |
**Table Details:**
- The table describes the probabilities of different combinations of deductibles for a homeowner’s and an automobile policy.
- For example, the value 0.20 in the first row and first column indicates that 20% of customers have a deductible of $200 for their homeowner's policy and $0 for their automobile policy.
**Questions:**
a. **What proportion of customers have $500 deductible amounts for both types of policies?**
- The probability of both deductibles being $500 is 0.30 or 30%.
b. **What proportion of customers have both deductible amounts less than $500?**
- The probability of both deductibles being less than $500 is the sum of the probabilities for \((x, y) = (200, 0)\), \((200, 250)\), and \((500, 0)\):
\[
0.20 + 0.10 + 0.05 = 0.35 \text{ or } 35\%
\]
c. **What is the marginal mass function of \( x \)? What is the marginal mass function of \( y \)?**
- **Marginal mass function of \( x \):**
- For \( x = 200 \), \( f(x = 200) = 0.20 + 0.10 + 0.20 = 0.50 \)
- For \( x = 500 \), \( f(x = 500) = 0.05 + 0.15 + 0.30 =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd627e045-d503-4693-9754-e0a854927fd5%2F5fe8e994-8e4e-4536-9d97-0029d9132c9e%2Fc7kb4tg_processed.png&w=3840&q=75)
Transcribed Image Text:**Educational Website Content:**
---
**Topic: Understanding Joint Mass Functions in Insurance**
**Introduction:**
A large insurance agency provides services to customers who have purchased both a homeowner's policy and an automobile policy. Each policy requires a specified deductible amount. Let \( x \) represent the homeowner’s deductible, and \( y \) represent the automobile deductible for customers with both policies.
**Joint Mass Function Explanation:**
The joint mass function \( f(x, y) \) is given as follows:
| \( x \) \\ \( y \) | 0 | 250 | 500 |
|---------------------|------|------|------|
| 200 | 0.20 | 0.10 | 0.20 |
| 500 | 0.05 | 0.15 | 0.30 |
**Table Details:**
- The table describes the probabilities of different combinations of deductibles for a homeowner’s and an automobile policy.
- For example, the value 0.20 in the first row and first column indicates that 20% of customers have a deductible of $200 for their homeowner's policy and $0 for their automobile policy.
**Questions:**
a. **What proportion of customers have $500 deductible amounts for both types of policies?**
- The probability of both deductibles being $500 is 0.30 or 30%.
b. **What proportion of customers have both deductible amounts less than $500?**
- The probability of both deductibles being less than $500 is the sum of the probabilities for \((x, y) = (200, 0)\), \((200, 250)\), and \((500, 0)\):
\[
0.20 + 0.10 + 0.05 = 0.35 \text{ or } 35\%
\]
c. **What is the marginal mass function of \( x \)? What is the marginal mass function of \( y \)?**
- **Marginal mass function of \( x \):**
- For \( x = 200 \), \( f(x = 200) = 0.20 + 0.10 + 0.20 = 0.50 \)
- For \( x = 500 \), \( f(x = 500) = 0.05 + 0.15 + 0.30 =
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