Let {Xn }n≥0 be a Markov chain with state space E = {0, 1, . . .} and transition probabilities given by:
p0,0= 1−p0,1=(3/4)
pi,i+1 =(1/2)( 1−(1/(i+2))) ∀i≥0
pi,i−1 = (1/2)( 1+(1/(i+2))) ∀i≥1
Determine whether the chain is transient, null recursive, or positive recursive. In the latter case, find the stationary distribution.