Question

The number of page requests that arrive at a Web server is a Poisson random variable with an average of 100 requests per minute. Find the probability that there are no requests in a 100-ms period.

(A) 0.368: The probability of no requests in a 100-ms period is approximately 0.368.
(B) 0.632: The probability of no requests in a 100-ms period is approximately 0.632.
(C) 0.135: The probability of no requests in a 100-ms period is approximately 0.135.
(D) 0.865: The probability of no requests in a 100-ms period is approximately 0.865.

Answer 1

The probability that there are no requests in a 100-ms period is approximately 0.9048.

Step-by-step explanation:

To find the probability that there are no requests in a 100-ms period, we need to use the Poisson distribution formula. The Poisson distribution formula is given by P(x) = (e^(-lambda) * lambda^x) / x!, where lambda is the average number of events per interval and x is the number of events. In this case, lambda is 100 requests per minute and x is 0 requests in a 100-ms period. Plugging in the values, we get P(0) = (e^(-100/1000) * (100/1000)^0) / 0! = e^(-0.1) = 0.9048. Therefore, the probability that there are no requests in a 100-ms period is approximately 0.9048.