Three frogs are playing near a pond. When they are in the sun they get too hot and jump in the lake at rate 1. When they are in the lake they get too cold and jump onto the land at rate 2. Let Xt be the number of frogs in the sun at time t .

(a) Find the stationary distribution for Xt .

(b) Check the answer to

(a) by noting that the three frogs are independent two-state Markov chains.