Consider telephone operator who, on the average, handles ve calls every 3 minute. (1) Can we use Poisson to model the number of calls in a minute? Briey explain. (2) What is the parameter if we focus on the number of calls in 15 minute? 30 minute? (3) The parameter of the number of calls 3 minute in 5. The probability of no calls in the next 3 minutes. P(X = 0), can be calculated by (e550)f(0!). Use the following code in python to get the corresponding probability. import scipy.stats as stats P = stats.poisson.pmf(o, 5) print(P) In general, with parameter A, the probability of exact a occurrences (pmf) can be calculated by import scipy.stats as stats P = stats.poisson.pmf(a, A) print(P) (4) What is the probability of 10 calls in the next 6 minutes? (5) The probability of the number of less than 10 calls in the next 6 minutes, P (X s. 10) can be calculated by the following code import scipy.stats as stats P1 = stats.poisson.cdf(10, 10) print(P1) In general, with parameter A, the probability of less than or equal to a occurrences (cdf) can be calculatec by import scipy.stats as stats P = stats.poisson.cdf(a, A) print(P) (6) What is the probability of less than or equal to 12 calls in the next 12 mins? What is the probability of less than 12 calls in the next 12 mins? What is the probability 12 calls in the next 12 mins? Is there a relationship between these three values? (7) What is the probability of more than 12 calls in the next 12 mins? (8) Calculate P (6 5. X a 15) in the next 12 mins