A population consists of Xn individuals at times n = 0, 1, 2, . . .. Between time n and time n 1 each of these individuals dies with probability p independently of the others; and the population at time n 1 consists of the survivors together with an independent random Poisson() number of immigrants. Let X0 have arbitrary distribution. What happens to the distribution of Xn as n ? [Hint: Remember for a MC if X0 and X1 , then is a stationary distribution. If X0 has Poisson() distribution for some > 0, what is the distribution of X1?]