A Markov Chain with a finite number of states is said to be regular if there exists a non negative integer n such that for any i, j ∈ S, P(n)i, j > 0 for any n >_ n.
(a) Prove that a regular Markov Chain is irreducible.
(b) Prove that a regular Markov Chain is aperiodic.

You eat 8 strawberries and your friend eats 12 strawberries from a bowl. there are 20 strawberries left. which equation and solution give the original number of strawberries?

Atype of plant is introduced into an ecosystem and quickly begins to take over. a scientist counts the number of plants after mmonths and develops the equation p(m)= 19.3(1.089)^m to model the situation. most recently, the scientist counted 138 plants.assuming there are no limiting factors to the growth of the plants, about how many months have passed since the plants werefirst introduced? a)o 6.1b)0.6.6c)10 72d)o 23.1

The party planning committee has to determine the number of tables needed for an upcoming event. if a square table can fit 8 people and a round table can fit 6 people, the equation 150 = 8x + 6y represents the number of each type of table needed for 150 people.