Inferential Statisticshard
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Consider a random variable XX with density f(xθ)=θxθ1f(x|\theta) = \theta x^{\theta-1} for x(0,1)x \in (0, 1). Using the method of moments, we find θ^MM=Xˉ1Xˉ\hat{\theta}_{MM} = \frac{\bar{X}}{1-\bar{X}}. How does the variance of this estimator behave as nn \to \infty compared to the Cramer-Rao Lower Bound (CRLB)?