We define the Markov chain { , n = 1,2,... } by where X 1 ,X 2 ,... is an infinite sequence of independent random variables having a binomial distribution with parameters n = 2 and p=l/2 (a) Calculate...

We define the Markov chain {, n = 1,2,... } by

where X₁,X₂,... is an infinite sequence of independent random variables having a binomial distribution with parameters
n = 2
and
p=l/2

(a) Calculate the transition matrix of the Markov chain.

(b) For every class of the chain, establish whether it is recurrent or transient. Justify.

(c) What is the distribution of the random variable
Y₂?