Markov chains problem please show complete work

PROBLEM 10.2. A frog is on one of the three lilly pads shown in the figure (labeled 1, 2 and 3) 3 that are located at the vertices of a 30-60-90 triangle. Every day the frog jumps to a new lilly pad, with a probability that is inversely proportional to its distance. If X,E{1, 2, 3} denotes the frog location on day k, then X, is a Markov chain. Draw the state-transition diagram. (b Is the chain irreducible and aperiodic? 2 (c) Find the probability transition matrix P. (d Find a pmf vector It = [ ], 2, It3 ] satisfying the balance equation It = It P. Find the long-term proportion of time that the frog spends on lilly pad 3