Assume that the number of alpha particles emitted in one second by a particular radioactive source has a Poisson distribution with parameter μ. Consider estimating μ based on a random sample X₁, X₂, …, X_n.
a. Find the Fisher information in a single observation using both (7.5) and (7.6).

Equation (7.5)

Equation (7.6)

b. Find the Cramér–Rao lower bound for the variance of an unbiased estimator of μ.
c. Determine the mle of μ and show that the mle is an efficient estimator.
d. Is the asymptotic distribution of the mle in accord with the last theorem of this section? Explain.

Transcribed Image Text:

E|-000 In (f(X; 0)) I(0) = E