In a study done at the National Institute of Science and Technology (Steel et al
ID: 3375558 • Letter: I
Question
In a study done at the National Institute of Science and Technology (Steel et al. 1980), asbestos fibers on filters were count as part of a project to develop measurement standards for asbestos concentration. Asbestos dissolved in water was spread on a filter, and punches of 3-mm diameter were taken from the filter and mounted on a transmission electron microscope. An operator counted the number of fibers in each of 23 grid squares, yielding the following counts: 31 29 19 18 31 28 34 27 34 30 16 18 26 27 27 18 24 22 28 24 21 17 24 Assume that the Poisson distribution with unknown parameter A would be a plausible model for describing the variability from grid square to grid square in this situation. a. Use the method of maximum likelihood to estimate the parameter A. b. Use the asymptotic properties of the maximum likelihood estimates to construct a 95% confidence interval for ?. As is approximately standard normal, where I(8) is the Fisher a reminder, for large samples the distribution of information.Explanation / Answer
we know that if x follows poisson distribution with mean lambda then the MLE of labda is mean of x
> x<-c(31,29,19,18,31,28,34,27,34,30,16,18,26,27,27,18,24,22,28,24,21,17,24)
> x
[1] 31 29 19 18 31 28 34 27 34 30 16 18 26 27 27 18 24 22 28
[20] 24 21 17 24
> mean(x)
[1] 24.91304