In Exercise 9.17, suppose that the populations are
Chapter 9, Problem 18E(choose chapter or problem)
In Exercise 9.17, suppose that the populations are normally distributed \(with\sigma_{1}^{2}=\sigma_{2}^{2}=\sigma^{2}\). Show that
\(\frac{\sum_{i=1}^{n}\left(X_{i}-\bar{X}\right)^{2}+\sum_{i=1}^{n}\left(Y_{t}-\bar{Y}\right)^{2}}{2 n-2}\)
is a consistent estimator of \(\sigma^{2}\).
Equation Transcription:
Text Transcription:
sigma_{1}^{2} = sigma_{2}^{2} = sigma^2
frac{sum_{i=1}^{n}(X_{i}-bar{X})^2 + sum_{i=1}^{n}(Y_{t}-\bar{Y})^2}{2 n-2}
sigma^2
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