Question

Suppose that the log-ons to a computer network follow a Poisson process with an average of 3 counts per minute.

Answer 1

Answer:

a) 20 second

b) 20 second

c) 1 minute

Step-by-step explanation:

Let X be the exponential random variable arising from the Poisson process with the rate λ = 3 counts per minute. Its cdf is then given by:  

F(x) = I - e^-3x, x >= 0  

Calculate the mean and the standard deviation of the random variable X as follows:  

Е(X) =I/λ =I/3=20 second

std (x) =√1/λ^2=1/3=20 second

For the part c), write down the equation:

0.95 = P(X < x) = F(x) = I - e^-3x

and solve the equation for x to obtain:

x = -1/3 In 0.05 = 0.9985 ≅  1 minute