Question

Calls to a telephone system follow a poisson distribution with a mean of five calls per minute. (a) What is the name applied to the distribution and parameter values of the time until the tenth call? (b) What is the mean time until the tenth call? (c) What is the mean time between the ninth and tenth calls?

Answer 1

The distribution and parameter values of the time until the tenth call follows a Gamma distribution with parameters n = 10 and λ = 5. The meantime until the tenth call is 2 minutes. The mean time between the ninth and tenth calls is also 2 minutes.

Step-by-step explanation:

(a) The name applied to the distribution of the time until the tenth call is called the Gamma distribution with parameters n = 10 and λ = 5. The Gamma distribution is a continuous probability distribution that is commonly used to model waiting times. In this case, the parameter n represents the number of events (calls), and λ represents the average rate at which the events (calls) occur. (b) The mean time until the tenth call can be calculated using the formula for the mean of the Gamma distribution: μ = n/λ. In this case, n = 10 and λ = 5, so the mean time until the tenth call is μ = 10/5 = 2 minutes. (c) The mean time between the ninth and tenth calls is equal to the mean time until the tenth call, which is 2 minutes.