A consumer electronics dealer sells new flat panel televisions for $1,000. The dealer offers customers a 4-year warranty. The warranty provides free replacement of a television that fails within the 4-year warranty period, but does not cover the cost of a replaced TV. 

The dealer discloses that 5% of new flat panel televisions fail during their first year of life, 10% of 1-year-old televisions fail during their second year of life, 15% of 2-year-old televisions fail during their third year of life, and 20% of 3-year-old televisions fail during their fourth year of life. Suppose that the dealer sells a consumer a 4-year warranty for $140 along with the television. 

(a) Model the 4-year warranty experience of the dealer as a sixstate absorbing multichain with two absorbing states. Choose one absorbing state to represent the replacement of a TV, which has failed during the warranty period, and the other to represent the survival of the TV until the end of the warranty period. Choose the transient states to represent the age of the television. Construct the transition probability matrix.

(b) What is the probability that the TV will have to be replaced during the warranty period?

(c) What is the dealer’s expected revenue from selling a 4-year warranty?