Ask Question
17 August, 22:51

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

(a) What is the mean time between counts (in minutes) ? (Round yours answers to 3 decimal places.)

(b) What is the standard deviation between counts (in minutes) ? (Round yours answers to 3 decimal places.)

(c) If it is an average of 3 counts per minute, find the value of x such that P (X < x) = 0.95 (Round yours answers to 4 decimal places.)

+2
Answers (1)
  1. 17 August, 23:32
    0
    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
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “Suppose that the log-ons to a computer network follow a Poisson process with an average of 3 counts per minute. (a) What is the mean time ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers