The discussion focuses on demonstrating that \(\hat{b} = -\frac{\sum \ln x_i}{n}\) is an unbiased estimator for the parameter \(b\). The probability density function is defined as \(f(x) = \frac{1}{b} e^{(1-b)/b}\). A critical point raised is the need to clarify whether the expression should be \((1-b)/b\) instead of \(1-b/b\), as the latter simplifies to \(1/b\), indicating a uniform distribution. The expected value of \(\hat{b}\) must equal \(b\) to confirm its unbiased nature.
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DavidLiew said:If I want shows that \hat{b} is an unbiased estimator for the b
where \hat{b} = - \sum ln xi /n
f(x)= \frac{1}{b} e(1-b/b)