Reference no: EM1311714
Let X be a Poisson random variable with probability density function:
p (x) = λx e-λ/x! When x = 0, 1, 2, 3, ...
Where the parameter λ > 0,
For this random variable
Consider a random sample of size n from the X distribution, and let
Y =∑I Xi, be the sample sum.
a. Show that Y/n is a maximum likelihood estimator of λ.
b. Show that the estimator in part (a) is unbiased and consistent.
c. Also, show that Y/n is an efficient estimator of λ.
d. In 1980, asbestos fibers on filters were counted as part of a project to develop measurement standards for asbestos concentration by the National Institute of Science and Technology. Twenty three random samples yielded 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
Assuming that the Poisson distribution is a plausible model in describing variability of asbestos fiber counts in filters; derive a 95% confidence interval indicating the variability in the average number in asbestos fibers.
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: Assuming that the Poisson distribution is a plausible model in describing variability of asbestos fiber counts in filters; derive a 95% confidence interval indicating the variability in the average number in asbestos fibers.
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