41. A customer has approached a bank for a $100,000one-year loan at an 8% interest rate. If the bank doesnot approve this loan application, the $100,000 will beinvested in bonds that earn a 6% annual return. Withoutadditional information, the bank believes that there is a4% chance that this customer will default on the loan,assuming that the loan is approved. If the customerdefaults on the loan, the bank will lose $100,000. Ata cost of $1000, the bank can thoroughly investigatethe customer’s credit record and supply a favorable orunfavorable recommendation. Past experience indicatesthat the probability of a favorable recommendation for acustomer who will eventually not default is 0.80, and thechance of a favorable recommendation for a customerwho will eventually default is 0.15a. Use a decision tree to find the strategy the bankshould follow to maximize its expected profit.b. Calculate and interpret the expected value of information (EVI) for this decision problem.c. Calculate and interpret the expected value of perfect information (EVPI) for this decision problem.d. How sensitive are the results to the accuracy ofthe credit record recommendations? Are there any“reasonable” values of the error probabilities thatchange the optimal strategy
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
41. A customer has approached a bank for a $100,000
one-year loan at an 8% interest rate. If the bank does
not approve this loan application, the $100,000 will be
invested in bonds that earn a 6% annual return. Without
additional information, the bank believes that there is a
4% chance that this customer will default on the loan,
assuming that the loan is approved. If the customer
defaults on the loan, the bank will lose $100,000. At
a cost of $1000, the bank can thoroughly investigate
the customer’s credit record and supply a favorable or
unfavorable recommendation. Past experience indicates
that the probability of a favorable recommendation for a
customer who will eventually not default is 0.80, and the
chance of a favorable recommendation for a customer
who will eventually default is 0.15a. Use a decision tree to find the strategy the bank
should follow to maximize its expected profit.
b. Calculate and interpret the expected value of information (EVI) for this decision problem.
c. Calculate and interpret the expected value of perfect information (EVPI) for this decision problem.
d. How sensitive are the results to the accuracy of
the credit record recommendations? Are there any
“reasonable” values of the error probabilities that
change the optimal strategy
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