. Let Xn denote the number of visitors at a certain web site (e.g., a food recipe site) at time n. At each time period, each visitor at the site independently leaves with probability p, and the number...

. Let
_Xn
denote the number of visitors at a certain web site (e.g., a food recipe site) at time n. At each time period, each visitor at the site independently leaves with probability p, and the number of new visitors that enter the site has a Poisson distribution with mean λ (independent of everything else). Show that
_Xn
is a Markov chain and determine its transition probabilities. Find a condition on p and λ under which the chain is ergodic. Show that its stationary distribution is a Poisson distribution and specify its mean.