Four years ago, Victor Consuelo purchased a very reliable automobile (as rated by a reputable consumer advocacy publication). His warranty has just expired, but the manufacturer has just offered him a 5-year, bumper-to-bumper warranty extension. The warranty costs $3,400.
Consuelo constructs the following probability distribution with respect to anticipated costs if he chooses not to purchase the extended warranty.
Cost (in $) ... Probability
1,000 ..... 0.25
2,000 ..... 0.45
5,000 ...... 0.20
10,000 .... 0.10

a. Calculate Victor’s expected cost.
b. Given your answer in part a, should Victor purchase the extended warranty? (Assume risk neutrality.) Explain.