An electronics retailer offers an optional protection plan for a mobile phone it sells. Customers can choose to buy the protection plan for $100, and in case of an accident, the customer pays a $50 deductible and
the retailer will cover the rest of the cost of that repair. The typical cost to the retailer is $200 per repair,
and the plan covers a maximum of 3 repairs.
Let X be the number of repairs a randomly chosen customer uses under the protection plan, and let F be
the retailer's profit from one of these protection plans. Based on data from all of its customers, here are the
probability distributions of X and F: