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.

What’s the answer ? use the picture to see the problem

In a test for esp (extrasensory perception), a subject is told that cards only the experimenter can see contain either a star, a circle, a wave, or a square. as the experimenter looks at each of 20 cards in turn, the subject names the shape on the card. a subject who is just guessing has probability 0.25 of guessing correctly on each card. a. the count of correct guesses in 20 cards has a binomial distribution. what are n and p? b. what is the mean number of correct guesses in 20 cards for subjects who are just guessing? c. what is the probability of exactly 5 correct guesses in 20 cards if a subject is just guessing?

One positive integer is 2 less than another. the product of the two integers is 24. what are the integers