$2.$Suppose that you have analyzed thousands of approved loan applications and whether the loans were paid in full or resulted in default. You have developed a model that uses the application data to predict whether the loan would result in default or full payment. The model has been applied to a hold out sample of $2,000$ loans to see how it would perform in practice. The results are summarized in the confusion matrix below. In this setting, we consider a $$positive$$ outcome to be paid in full.

Prediction$\backslash$Truth Paid Default Total

Paid $1,763431,806$

Default $85109194$

Total $1,8481522,000$

b$.$What is the $$sensitivity rate$$ for the model? Explain the meaning of this $$sensitivity rate$$ in words the bank manager would understand.

c$.$What is the $$specificity rate$$ for the model? Explain the meaning of this $$specificity rate$$ in words the bank manager would understand.

d$.$ What is the $$false omission rate$$ for the model? Explain the meaning of this $$false omission rate$$ in words the bank manager would understand.

e$.$What is the $$false detection rate$$ for the model? Explain the meaning of this $$false detection rate$$ in words the bank manager would understand