unbiased estimator for ? and provide an estimate for the
Chapter 8, Problem 36E(choose chapter or problem)
If \(Y_{1^{\prime}} Y_{2}, \ldots, Y_{n}\) denote a random sample from an exponential distribution with mean \(\theta\), then \(\theta\) and \(V\left(Y_{i}\right)=\theta^{2}\). Thus, \(E\left(Y^{-}\right)=\theta\) and \(V\left(Y^{-}\right)=\theta^{2} / n\), or \(\sigma_{y^{-}}=\theta / \sqrt{n}\) Suggest an unbiased estimator for and provide an estimate for the standard error of your estimator.
Equation Transcription:
Text Transcription:
Y_1,Y_2 ,...,Y_n
theta
E(Y_i)=theta
V(Y_i)=theta^2
E(Y^-)=theta
V(Y^-)=theta^2/n
sigma_Y-=theta/sqrt n
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