Problem 2E

The time between requests to a web server is exponentially distributed with mean 0.5 seconds.

a. What is the value of the parameter λ?

b. What is the median time between requests?

c. What is the standard deviation?

d. What is the 80th percentile?

e. Find the probability that more than one second elapses between requests.

f. If there have been no requests for the past two seconds, what is the probability that there more than one additional second will elapse before the next request?

Solution

Step 1 of 7

Here time is exponentially distributed with mean 0.5 seconds

Then =0.5

The Pmf of exponential distribution is

The CDF of exponential distribution is