Question: 3. A computer processes two kinds of requests. One is an on-line query and the other is a request to run an application program.

3. A computer processes two kinds of requests. One is an on-line query and the other is a request to run an application program. The queries arrive according to a Poisson process at a rate of 90 per hour. The run requests arrive according to an independent Poisson process at a rate of 10 per hour. Answer the following questions a. What is the expectation of the total number of requests (online and run) to arrive between 8:00 am and 10:00 am? b. If 60 queries arrive between 9:00 am and 9:30 am, what is the expectation of the number of run requests for that same time period? c. If 25 queries arrive between 10:00 am and 10:30 am, what is the expectation of the total number of queries for 10:00 am to 11:00 am? d. If 8 run requests arrive between 1:00 pm and 1:30 pm, what is the probability that no requests will arrive between 1:30 pm and 1:40 pm? e. If the last run request was 20 minutes ago and the last query was 5 minutes ago, what is the probability that no requests (run or query) will occur in the next two minutes?

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