Question

An electronics retailer offers an optional protection plan for a mobile phone it sells. Customers can choose to buy the protection plan for \$100$100dollar sign, 100, and in case of an accident, the customer pays a \$50$50dollar sign, 50 deductible and the retailer will cover the rest of the cost of that repair. The typical cost to the retailer is \$200$200dollar sign, 200 per repair, and the plan covers a maximum of 333 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:

X=\# \text{ of repairs}X=# of repairsX, equals, \#, start text, space, o, f, space, r, e, p, a, i, r, s, end text 000 111 222 333

F=\text{ retailer profit}F= retailer profitF, equals, start text, space, r, e, t, a, i, l, e, r, space, p, r, o, f, i, t, end text \$100$100dollar sign, 100 -\$50−$50minus, dollar sign, 50 -\$200−$200minus, dollar sign, 200 -\$350−$350minus, dollar sign, 350

Probability 0. 900. 900, point, 90 0. 70. 070, point, 07 0. 20. 020, point, 02 0. 10. 010, point, 01

Find the expected value of the retailer's profit per protection plan sold

Answer 1

To calculate the expected value of the retailer's profit per protection plan sold, multiply the profit for each possible outcome by its corresponding probability and sum up these values.

Step-by-step explanation:

The expected value of the retailer's profit per protection plan sold can be calculated by multiplying the profit for each possible outcome by its corresponding probability, and then summing up these values. In this case, the profit for each outcome is given by the difference between the cost to the retailer and the deductible paid by the customer. The expected value of the profit is then:

E(F) = (100 - 50) * 0.90 + (100 - 50) * 0.07 + (-200 - 50) * 0.02 + (-350 - 50) * 0.01

Calculating this expression gives the expected value of the retailer's profit per protection plan sold.