*10. (Pfifer and Carraway, 2000) A company targets its customers through direct mail advertising.

During the first year, the probability that the customer will make a purchase is .5, which reduces to .4 in year 2, .3 in year 3, and .2 in year 4. If no purchases are made in four consecutive years, the customer is deleted from the mailing list. Making a purchase resets the count back to zero.

(a) Express the situation as a Markov chain.