Find the probability that more than 25 requests are

Question

In a one minute interval, the number of requests for access to a web-based game is a Poisson random variable with a mean of 20.

(a) Find the probability that more than 25 requests are received in the one minute interval by applying the central limit theorem. (Hint: apply the de Moivre-Laplace approximation)

(b) Calculate the exact probability in part (a) using the Poisson random variable. Compare with the result you obtained in part (a). (Hint: use Matlab to code the Poisson PMF)

(c) The web game server has a capacity for C requests per minute. If the number of requests exceed C, the server is overloaded. Apply the central limit theorem to estimate the smallest value of C for which the probability of overload is less than 0.05.

(d) Use MATLAB to calculate the actual probability of overload for the value of C derived from the central limit theorem in part (c).

(e) For the value of C derived from the central limit theorem, what is the probability of overload in a one-second interval?

(f) Comment on the application of the central limit theorem to estimate the overload probability in the one-second interval versus that in the one-minute interval.

Answer 1

Consider the situation illustrated below and perform the tasks as given as per guidelines. In a 1 minute interval, the number of requests for access to the web-based game is a Poisson random variable by means of a mean of 20. 1) Determine the probability that more than 25 requests are received in the 1 minute interval by implementing the central limit theorem. 2) Compute the exact probability in part (1) employing the Poisson random variable. Compare by means of the outcome you obtained in part (1). 3) The web game server consists of a capacity for C requests per minute. If the number of requests surpasses C, the server is overloaded. Implement the central limit theorem to approximate the smallest value of C for which the probability of overload is less than 0.05. 4) Make use of MATLAB to compute the actual probability of overload for the value of C derived from the central limit theorem in part (3).