Finally, as the training sample was oversampled for buyers, the predicted purchase probabilities for customers in the representative sample should be adjusted as described in page 6 to get the true purchase probabilities for calculating the correct expected profits for each department. After adjusting the purchase probabilities, use the following formula to calculate customers' expected profit for each department: Expected Profit from a customer for a department's e-mail message = Department-specific Profit Margin Percentage (e.g., 45% for Backcountry) * Predicted Order Size of the customer for that department's e-mail message * True Purchase Probability of the customer for that department HINT: You should find that the Backcountry department's message maximizes the expected profit for 9.85% of the customers. Q4. (1 point) Use the calculated expected profits in question 3 to answer the following. a. For each department, report the expected profit per e-mailed customer if all customers receive an e-mail message from the department. HINT: You should find that this is 2.67 cents for the Backcountry department. b. If customers are randomly assigned to the five departments, then the expected profit per e-mailed customer will simply be the average of the five numbers reported in 4a above. Report this average value. How does this number compare with the expected profit per e-mailed customer if we personalize the message to each customer to maximize the expected profit? c. For the typical promotional e-mail blast to 5,000,000 customers per week, how much improvement in total profit does Pentathlon expect to obtain from customizing the message to each customer rather than assigning customers a message at random? Report the improvement as a dollar value