Answer Happy

We assume that the number of individuals who are infected by a carrier of a disease is a random variable from a Poisson distribution with an unknown parameter > 0. We have observed that 750 randomly chosen, infected individuals transmitted the disease to a total of 3750 new persons. • A researcher wishes to construct a 1 - a = 99% confidence interval for the parameter 1. An asymptotic procedure of constructing an approximate confidence interval based on the maximum likelihood estimator î of is used, i.e. À À + -). Based on the available information, we conclude that the Vn (4) Vnha value* of the maximum likelihood estimator of 1 for the sample amounts to  = the value* U1-a/2 U1-a/2 2 of the maximum likelihood estimator of the Fisher Information connected with the sample amounts to MLE(In(\)) = so the realization of the confidence interval for for this sample is: ( • A different researcher wishes to construct a 1-a = 99% confidence interval for the average number of persons to which an infected individual transmits the disease. Since detailed information about the variability of the number of transmissions is not available (other than stated above), the researcher approximates the sample variance with the sample mean and then proceeds to construct the confidence interval in a standard way. The realization of the confidence interval for the average number of transmissions of an individual in this case is equal to: ( Comparing the confidence interval constructed for in the previous point with the confidence interval constructed for the mean in this point, we can say that: