How do you calculate the marginal numbers in this chart? **Understanding Credit Risk Analysis in Financial Institutions****Introduction**Credit risk assessment is a critical component for financial institutions in issuing credit cards. Using statistical data and discriminant analysis, credit card companies aim to identify applicants who are likely to be responsible with credit.**Industry Statistics**A credit card company has identified through industry statistics that:- 80% (or 0.8) of potential cardholders are considered good credit risks.- 20% (or 0.2) of potential cardholders are considered bad credit risks.**Screening Process**To determine which applicants should receive credit cards, the company employs discriminant analysis. **Approval Rate**- Credit cards are awarded to 70% of applicants.**Good Credit Risk Outcomes**- Among the awarded credit cards, 95% of the recipients turn out to be good credit risks.**Problem Statement**Given this information, the task is to determine the probability that an applicant who is a bad credit risk will be denied a credit card.This example illustrates the application of probability and discriminant analysis in real-world financial decision-making by illustrating how financial institutions balance approval rates with risk management to minimize the issuance of credit cards to high-risk individuals. ### Understanding Conditional ProbabilityAccording to the provided information of the problem and by using the definition of conditional probability, the following table can be constructed:| | Credit Risk Good | Credit Risk Bad | Marginal ||--------------------|------------------|-----------------|----------|| **Credit Awarded** | 0.665 | 0.035 | 0.7 || **Credit Denied** | 0.135 | 0.165 | 0.3 || **Marginal** | 0.8 | 0.2 | |#### Explanation of the Table:- **Credit Awarded** and **Credit Denied** represent the decisions made regarding the applicants' credit requests. - **Credit Risk Good** and **Credit Risk Bad** represent the categorization of applicants based on their creditworthiness.- The **Marginal** column/row represents the marginal probabilities of awarding or denying credit without considering the credit risk.- The values in the table represent the conditional probabilities. For example: - 0.665 is the probability of awarding credit given that the credit risk is good. - 0.035 is the probability of awarding credit given that the credit risk is bad.- The marginal probabilities sum to 1. For example: - The sum of the probabilities for Credit Awarded and Credit Denied equals 1 (0.7 + 0.3). - The sum of the probabilities for Credit Risk Good and Credit Risk Bad equals 1 (0.8 + 0.2).This table provides a comprehensive view of how likely credit is to be awarded or denied, given the applicants' credit risk profiles.

Given information- We have given the table- Credit Risk Good Bad Marginal Credit…

From industry statistics, a credit card company knows that 0.8 of its potential card holders are good credit risks and 0.2 are bad credit risks. The company uses discriminant analysis to screen credit card applicants and determine which ones should receive credit cards. The company awards credit cards to 70% of those who apply. The company has found that of those awarded credit cards, 95% turn out to be good credit risks. What is the probability that an applicant who is a bad credit risk will be denied a credit card?

From industry statistics, a credit card company knows that 0.8 of its potential card holders are good credit risks and 0.2 are bad credit risks. The company uses discriminant analysis to screen credit card applicants and determine which ones should receive credit cards. The company awards credit cards to 70% of those who apply. The company has found that of those awarded credit cards, 95% turn out to be good credit risks. What is the probability that an applicant who is a bad credit risk will be denied a credit card?

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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Question

How do you calculate the marginal numbers in this chart?

**Understanding Credit Risk Analysis in Financial Institutions**

**Introduction**
Credit risk assessment is a critical component for financial institutions in issuing credit cards. Using statistical data and discriminant analysis, credit card companies aim to identify applicants who are likely to be responsible with credit.

**Industry Statistics**
A credit card company has identified through industry statistics that:
- 80% (or 0.8) of potential cardholders are considered good credit risks.
- 20% (or 0.2) of potential cardholders are considered bad credit risks.

**Screening Process**
To determine which applicants should receive credit cards, the company employs discriminant analysis.

**Approval Rate**
- Credit cards are awarded to 70% of applicants.

**Good Credit Risk Outcomes**
- Among the awarded credit cards, 95% of the recipients turn out to be good credit risks.

**Problem Statement**
Given this information, the task is to determine the probability that an applicant who is a bad credit risk will be denied a credit card.

This example illustrates the application of probability and discriminant analysis in real-world financial decision-making by illustrating how financial institutions balance approval rates with risk management to minimize the issuance of credit cards to high-risk individuals.

### Understanding Conditional Probability

According to the provided information of the problem and by using the definition of conditional probability, the following table can be constructed:

| | Credit Risk Good | Credit Risk Bad | Marginal |
|--------------------|------------------|-----------------|----------|
| **Credit Awarded** | 0.665 | 0.035 | 0.7 |
| **Credit Denied** | 0.135 | 0.165 | 0.3 |
| **Marginal** | 0.8 | 0.2 | |

#### Explanation of the Table:

- **Credit Awarded** and **Credit Denied** represent the decisions made regarding the applicants' credit requests.
- **Credit Risk Good** and **Credit Risk Bad** represent the categorization of applicants based on their creditworthiness.
- The **Marginal** column/row represents the marginal probabilities of awarding or denying credit without considering the credit risk.
- The values in the table represent the conditional probabilities. For example:
- 0.665 is the probability of awarding credit given that the credit risk is good.
- 0.035 is the probability of awarding credit given that the credit risk is bad.
- The marginal probabilities sum to 1. For example:
- The sum of the probabilities for Credit Awarded and Credit Denied equals 1 (0.7 + 0.3).
- The sum of the probabilities for Credit Risk Good and Credit Risk Bad equals 1 (0.8 + 0.2).

This table provides a comprehensive view of how likely credit is to be awarded or denied, given the applicants' credit risk profiles.

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