What is the expected value of a single warranty?

Question

An electronics store sells extended warranties. For a particular product they estimate 8% of those who buy the $14 warranty will use it, costing the store $110 to replace and ship the product. What is the expected value of a single warranty?

Answer 1

 

 

There are two values for the random variable, either they payout the cost to replace or they don't, so:

 

Let X = Payout

 

Take in 110 for the original cost, plus the warranty of 14 paid, minus the cost to replace = 14 @ .08

Take in 110 for the original cost, plus the warranty of 14 paid, minus nothing as that happens .92 or 92% of time:

 

X       p (x)

 

14     .08

124   .92

 

The expected value of the payout on a warranty is mu = E(X) = 14 * .08 + 124 * .92  = 1.12 + 114.08 = $115.20