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 the time between requests is between 1 and 2 seconds. Probabili

Answer 1

11.7% probability that the time between requests is between 1 and 2 seconds.

Explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

`f(x) = \mu e^(-\mu x)`

In which
`\mu = (1)/(m)` is the decay parameter.

The probability that x is lower or equal to a is given by:

`P(X \leq x) = \int\limits^a_0 {f(x)} \, dx`

Which has the following solution:

`P(X \leq x) = 1 - e^(-\mu x)`

In this problem, we have that:

`m = 0.5, \mu = (1)/(m) = 2`

Find the probability that the time between requests is between 1 and 2 seconds.

`P(1 \leq X \leq 2) = P(X \leq 2) - P(X \leq 1)`

`P(X \leq 2) = 1 - e^(-2*2) = 0.9817`

`P(X \leq 1) = 1 - e^(-2*1) = 0.8647`

`P(1 \leq X \leq 2) = P(X \leq 2) - P(X \leq 1) = 0.9817 - 0.8647 = 0.117`

11.7% probability that the time between requests is between 1 and 2 seconds.