The arrival of requests to web server is described by a Poisson process with a rate of 120 request per minute. Write down the formula for the distribution of the inter-arrival time of requests in seconds. What is the probability that two requests will be separated by more than 1 second? Requests that arrive to that web server are queued up in a buffer until processed by a single-threaded HTTP server. Assuming that the time it takes the HTTP server to process a request on a given processor is exponential with an average of 400 milliseconds. (1) Write down the formula for the distribution of the total number of pending requests to the web server. What is the probability that the web server will be idle? (2) How many pending web requests do you expect to find in the system on average? What is the average response time for requests to the web server? (3) How much faster should the processor be in order to cut the response time by a third? (4) How much faster would the web server be if the HTTP server is re-engineered in a way that makes the time to process a request be highly predictable almost a constant equal to 400 milliseconds? (5) Based on your answers above, provide justification for the following sentence: Blindly going for faster hardware to improve performance may be what most practitioner do, but it should not be what an informed computer scientist should do"