Question

The time between requests to a web server is exponentially distributed with mean 0.5 seconds. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Find the probability that there will be exactly 5 requests in a 2-second time interval.

Answer 1

Probability that there will be exactly 5 requests is 0.156

Step-by-step explanation:

Poisson probability will be used to solve this problem

`P(X=x) =(\lambda^(x)e^(-\lambda) )/(x!)`...............(1)

`\lambda = (2)/(0.5) \\\lambda = 4`

Probability that there will be exactly 5 requests in a 2 second time interval

x = 5

Substituting the values of x and λ into equation (1)

P(X = 5) =
`(4^(5) e^(-4) )/(5!)`

P(X=5) = 0.156