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Consider a random sample of size n from a Poisson distribution, Xi ~ POI(m).
a) Find the CRLB for the variances of unbiased estimators of m.
b) Find the CRLB for the variances of unbiased estimators of theta = e^(-m).
c) Find the UMVUE of m.
d) Find the MLE theta(hat) of theta.
e) Is theta(hat) an unbiased estimator of theta?
f) Is theta(hat) asymptotically unbiased?
g) Show that theta~ = [(n-1)/n]^(sum Xi) is an unbiased estimator of theta.
h) Find Var(theta~) and compare to the CRLB of b).
Is sample of 25 papers large adequate to give a good estimate of mean score of all 42,000 students on this exam problem? Explain your answer.
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Five students took a math test before and after tutoring. Their scores were as follows. Using a 0.01 level of significance, test the claim that the tutoring has an effect on the math scores.
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