Two dogs - Lisa and Cooper - share a population of N fleas. Fleas jump from one dog to another independently at rate per minute. Let Xt denote the number of fleas on Lisa at time t (measured in minutes). We assume that (Xt)t>=0 is a birth-and-death process. Suppose there are x = 0, 1, . . . , N fleas on Lisa at time t = 0.

(a) Compute the expected number mx(t) of fleas on Lisa at time t > 0, i.e., find mx(t)= E[Xt | X0 = x].

Compute lim(t->infinity) E[Xt | X0 = x] i.e., the expected number of fleas on Lisa in the long-run.