Question: Web access pattern. Consider a web server that receives web access requests from a large number of users. We assume that the request arrival mechanism is characterized by the following simple model. We divide the time axis into contiguous segments of seconds, and is chosen sufficiently small that the probability of receiving more than one request is negligibly small. We also assume that the arrivals in different segments are statistically independent events. Let p be the probability that a randomly chosen segment interval observes an arrival of a request.
(a) Assume an observation interval of T = 5?, and let p = 0.2. What is the probability that at least two requests arrive during this observation interval?
(b) For any integer n = 1, 2, 3,..., find the probability that T = n? will be the observation interval required to see the first arrival.
(c) Suppose that you are informed that there are k successes in n Bernoulli trials. Obtain the conditional probability that any particular trial resulted in a success.