Let Xn denote the number of visitors at a certain web site (e.g., a food recipe

Question

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 (independent of everything else). Show that Xn is a Markov chain and determine its transition probabilities. Find a condition on p and under which the chain is ergodic. Show that its stationary distribution is a Poisson distribution and specify its mean.

Explanation / Answer

P = landha / xbar

Poisson distribution = mean = landha so

P = miu / xbar

P = proportion of sample

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