2. * A web page is accessed at an average of 20 times an hour. Assume that waiting time until the next hit has an exponential distribution. (a.) Determine the rate parameter ? of the distribution of the time until the first hit? (b.) What is the expected time between hits? (c.) What is the distribution of the time until the second hit? (Give the name of the distribution and the value(s) of parameter(s).) (d.) What is the probability that the next hit is within 20 minutes? (e.) Describe the distribution of the total waiting time for 5 hits? (Give the name of the distribution and the value(s) of parameter(s).) (f.) What is the expected total waiting time for 5 hits on the web page? (g.) What is the probability that there will be less than 5 hits in the first hour? (Hint: Consider Poisson distribution instead.)
Added by Salvador W.
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- The average rate of hits is 20 times per hour. Therefore, the rate parameter Ī» for the exponential distribution is 20 hits per hour. Show moreā¦
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A web page is accessed at an average of 20 times an hour. Assume that waiting time until the next hit has an exponential distribution. Determine the rate parameter Ī» of the distribution of the time until the first hit? What is the expected time between hits? What is the distribution of the time until the second hit? (Give the name of the distribution and the value(s) of parameter(s).) What is the probability that the next hit is within 20 minutes? Describe the distribution of the total waiting time for 5 hits? (Give the name of the distribution and the value(s) of parameter(s).) What is the expected total waiting time for 5 hits on the web page? What is the probability that there will be less than 5 hits in the first hour? (Hint: Consider Poisson distribution instead.)
David N.
A "hit" for a website is a request for a file from the website's server computer. Some popular websites have thousands of hits per minute. One popular website boasts an average of 6500 hits per minute between hours of 9 A.M. and 6 P.M. Assume that the hits per minute are well modeled by the Poisson distribution. a) What is the probability that exactly 1000 hits occur during a minute between 9 A.M. and 6 P.M? Write down the numerical expression and you don't need to find the final result. b) Use Excel's Poisson function to calculate the probability of 6400 or more hits during the minute beginning at 10 A.M. What did you get? c) Find the probability of part b) using the Normal approximation.
Audrey F.
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