Question

The conditional distribution of F given N = 1 is 0.1818

The conditional distribution of N given F= 4 is 0.8

f) Calculate the conditional expectation E(N | F = 4).

g) Consider the relationship between N and F.

1. Would you expect N and F to be independent? Explain your answer.
2. Based on the joint probability distribution, are N and F independent? Explain
3. What is a plausible strategy for targeting customers for promotions?

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:

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