Suppose that the recruitment of a new customer will cost you $50 per recruit through media ads, mail and email, coupons, etc. Let X denote the uncertain amount of sales that a recruited customer will generate. Suppose that the uncertainty distribution of the random variable X is as follows:
x $0 $10 $40 $100
Pr(X=x) 0.4 0.1 0.2 0.3 11.
What is the numerical value of the sales that a newly recruited customer can be expected to generate? Would you attempt to recruit new customers under these conditions? Why or why not?
Let Y = 1 if a customer generates less than $50 in sales, and Y = 0 if a customer generates $50 or more in sales.
What is the uncertainty distribution of Y? Write down all of the possible outcomes and their probabilities.