Refer to Exercise 9.21. Suppose that Y1, Y2, . . . , Yn is
Chapter 9, Problem 22E(choose chapter or problem)
Refer to Exercise 9.21. Suppose that \(Y_{1}, Y_{2}, \ldots, Y_{n}\) is a random sample of size from a Poisson-distributed population with mean \(\lambda\). Again, assume that \(n=2 k\) for some integer
. Consider
\(\hat{\lambda}=\frac{1}{2 k} \sum_{i=1}^{k}\left(Y_{2 i}-Y_{2 i-1}\right)^{2}\)
a Show that \(\hat{\lambda}\) is an unbiased estimator for \(\lambda\).
b Show that \(\hat{\lambda}\) is a consistent estimator for \(\lambda\).
Equation Transcription:
Text Transcription:
Y_1, Y_2, \ldots, Y_n
\lambda
n=2 k
\hat\lambda=\frac1 2 k \sum_i=1^k\left(Y_2 i-Y_2 i-1\right)^2
\hat\lambda
\lambda
\hat\lambda
\lambda
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