Question

A forest consists of two types of trees: those that are 0–5 ft and those that are taller than 5 ft.

• Each year, 40% of all 0–5 ft tall trees die, 10% are sold for $20 each, 30% stay between 0 and 5 ft, and 20% grow to be more than 5 ft.

• Each year, 50% of all trees taller than 5 ft are sold for $50, 20% are sold for $30, and 30% remain in the forest.

a) Define the states and write the transition matrix for this Markov chain.

b) Classify the states as transient, recurrent, absorbing, periodic, aperiodic.

c) How long is a newly planted (less than 5 ft) tree remain in the forest?

d) How long is a tree, which is just grown (more than 5 ft.), remain in the forest?

Answer 1