An online book publisher targets its subscribers through website mail advertising. The probability that the subscriber will make a subscription is 0.50 during the first year, which reduces to 0.40 in year 2, 0.30 in year 3, and 0.2 in year 4. If no subscriptions are made in four consecutive years, the subscriber is deleted from the mailing list. Making a subscription resets the count back to zero.
a) Establish the transition probability matrix. Answers in 3 decimal places.
b) Determine the expected number of years a new subscriber will be on the mailing list.
c) If a subscriber has not made a subscription in two years, determine the expected number of years on the mailing list.