Question

In target marketing, the goal is to target certain customers for promotions. A promotion might consist of mailing a special catalogue to a customer. Firms maintain large databases of information on their customers. One of the most useful variables is frequency of purchases; i.e., how often a customer makes a purchase. A customer is randomly chosen from the record of existing customers and sent a special catalogue. Let N represent a random variable that takes value 1 if a customer makes a new purchase and value 0 if otherwise. Let F be a random variable representing purchase frequency, where F takes on values {1, 2, 3, 4}. - A value of F = 1 indicates that 1 purchase was made within the last year. - A value of F = 2 indicates that 2 - 10 purchases were made within the last year. - A value of F = 3 indicates that 11 - 20 purchases were made within the last year. - A value of F = 4 indicates that more than 20 purchases were made within the last year. The marketing research department has determined that the joint probability distribution of (N,F) is given by the following table: N=0 N=1 F=1 0.08 0.02 F=2 0.36 0.24 F=3 0.10 0.10 F=4 0.02 0.08 a) CalculatePNF(1,2). b) Calculate and interpret pN (1). c) Calculate the marginal distribution of F, PF(f ). d) Calculate the conditional distribution of F given N = 1. e) Calculate the conditional distribution of N given F = 4. f) Calculate the conditional expectation E(N |F = 4). g) Consider the relationship between N and F. Would you expect N and F to be independent? Explain your answer. Based on the joint probability distribution, are N and F independent? Explain your answer. Briefly explain a plausible strategy for targeting customers for promotions, based on the work done in this problem. Use language accessible to someone who has not taken a statistics course and limit your explanation to at most five sentences.

Answer 1