Problem 4: Bad Debt encore (4 points) Reconsider the Bad Debt problem from Homework 1, and its accompanying dataset. The second column in the dataset provides the variable "Invoice amount". Suppose that the firm separates invoices into two categories: an invoice is "Small" if the invoice amount is less than $4,000, and it is "Large" if it is $4,000 or more. How would this firm estimate its bad debt? We answer this by performing the following steps. (a) Create two copies of the probability tree structure you used in Homework 1 (see below); label one tree as "Small" and one as "Large". Using the data from Homework 1 (BadDebt . x1s), fill in probability information for the "Small" tree using data on small invoices. Do the same for the "Large" tree using data on large invoices. (Hint: you are merely dividing the data into two sets, and doing two new versions of the same exercise you did in Homework 1!) Your answer should be two complete trees. (b) Using your trees, compute the following probabilities. (Use your "Small" tree for the first four, and your "Large" tree for the other four.) (i) P(Bad Debt | Small) = ? (ii) P(Bad Debt | Small AND not paid On Time) = ?_ P(Bad Debt | Small AND not paid in first 91 days) = ?_ (iv) P(Bad Debt | Small AND not paid in first 121 days) = ? (V) P(Bad Debt | Large) = ? ( vi) P(Bad Debt | Large AND not paid On Time) = ? (vii) P(Bad Debt | Large AND not paid in first 91 days) = ? (viii) P(Bad Debt | Large AND not paid in first 121 days) = ? (Note: Again this mirrors what you did in Homework 1. Your answer should list eight probabilities, clearly labeled.)