1. A Markov chain model for the growth and replacement of trees assumes that there are three stages of growth based on the size of the tree; young tree, mature, tree, and old tree. The transition period considered is 8 years. In each period of 8 years, 30% of the young trees remain young and the rest becomes mature. Among the mature trees 40% remain mature and the rest become old in 8 years. The probability that a old tree is replaced by a young tree in a 8 years period is p, 0 0, for all i&j 2 S, and hence calculate P(10) & M(10). (b) Specify an initial law~a = (ai) (distribution of the chain at n=0) (give numerical vector) such that ai > 0 for i 2 S, and hence calculate ~a(10) using the P specied in part (a). 3. A system consisting of two components is subject to a series of shocks . The time be- tween consecutive shocks can be modelled as independent…