A web page is accessed at an average of 10 times an hour. Assume that waiting ti

Question

A web page is accessed at an average of 10 times an hour. Assume that waiting time until the next hit has an exponential distribution and that the hits are independent of each other.

(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 10 minutes?

(e) Describe the distribution of the total waiting time for 10 hits? (Give the name of the distribution and the value(s) of parameter(s).)

(f) What is the expected total waiting time for 10 hits on the web page?

(g) What is the probability that there will be less than 3 hits in the first hour?

Explanation / Answer

Solutions:

(a) = 10

(b) 1/ = 1/10 hours = 6 minutes.

(c) Gamma( = 2, = 10)

(d) Evaluate the cdf of an Exp( = 10) distribution at t = 10:

1 e ^10·10 = 1 e ^100 1

(e) Gamma( = 10, = 10)

(f) / = 10/10 = 1 hour.

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