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# 2.21 Web access pattern: Consider a web server that receives web access requests from large number of users. We assume that the request arrival mechanism is charac-...

## Question

###### 2.21 Web access pattern: Consider a web server that receives web access requests from large number of users. We assume that the request arrival mechanism is charac- terized by the following simple model. We divide the time axis into contiguous segments of 4 seconds, and 4 is chosen sufficiently small that the probability of receiving more than one request is negligibly small We also assume that the arrivals in different seg- ments are statistically independent events_ Let p be the probability th

2.21 Web access pattern: Consider a web server that receives web access requests from large number of users. We assume that the request arrival mechanism is charac- terized by the following simple model. We divide the time axis into contiguous segments of 4 seconds, and 4 is chosen sufficiently small that the probability of receiving more than one request is negligibly small We also assume that the arrivals in different seg- ments are statistically independent events_ Let p be the probability that randomly chosen segment interval observes an arrival of a request_ (a) Assume an observation interval of T = 54_ and let p = 0.2. What is the probability that at least two requests arrive during - this observation interval? (b) For any integer 1,2,3_ find the probability that T =nA 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_

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