Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

Underwriters at a bank have estimated the probability that two personal mortgage loans will default in the next year, arranged in the probability table below

Underwriters at a bank have estimated the probability that two personal mortgage loans will default in the next year, arranged in the probability table below - the random variable X1 denotes the status of customer 1's loan, X2 denotes the status of customer 2's loan, and each random variable is 1 if the loan defaults and 0 otherwise.

X2 = 0 X2 = 1
X1 = 0 0.94 0.04
X1 = 1 0.01 0.01

1. What is the probability that loan 1 defaults?

2. Based on these probabilities do the underwriters consider the two random variables X1 and X2 to be independent?

3. The same bank also issued an auto loan to customers 1 and 2. Historically, the bank knows that 80% of customers who defaulted on their mortgages missed a car payment, while only 5% of customers who did not default on their mortgages miss a car payment. Customer 1 missed a car payment this month. After getting this new information, what is the probability (approximately) that he will default on his mortgage?

4. Now suppose it was customer 2 who missed a car payment this month. What is the probability that he will default on his mortgage in the next year?

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Elementary Differential Equations

Authors: William E Boyce, Richard C DiPrima, Douglas B Meade

11th Edition

1119169879, 9781119169871

More Books

Students also viewed these Mathematics questions

Question

What are the major advantages of dollar-value LIFO?

Answered: 1 week ago

Question

Discuss the role of home economics to national development.

Answered: 1 week ago