Suppose that you have just pruchased an appliance which you intend to own for the next 4 years.The appliance comes with a basic warranty that provides for full placement of the appliance if it breaks down within the first year of service, where the probability that the machine will breakdown in the first year is 0.05.

Under basic warranty repairs after the first year are covered by the owner. The probabily that the appliance needs repairs in years 2, 3 and 4 are given by 0.08, 0.11, and 0.16 repectively. The cost of a repair in year 2 is $150, the cost for repair in year 3 is $200 and in year 4 the cost of repair is $250

Model the ownership over the next 4 years as a DTMC $\displaystyle {X_n, n\ge 0}$ where $\displaystyle X_n$ is the age of the appliance in service at the beginning of year n.

(a) give the transition diagram

(b) For $80 you can get extended warranty which covers all costs for the 4 year period. Is this extended warranty worthwhile?