Teaching CSIR NET Mock Test Series Mathematical Science Statistics & Exploratory Data Analysis Sampling Distributions
For n ≥ 2, let X1, X2, ..., Xn be a random sample from a distribution with the probability density function
\(f(x \mid θ)=\left\{\begin{array}{cc} θ x^{θ-1}, & 0
where θ > 0 is an unknown parameter. Then which of the following is the uniformly minimum variance unbiased estimator for \(\frac{1}{\theta}\) ?
1
\(-\frac{1}{n} \sum_{i=1}^n \ln X_i\)
2
\(-\frac{n}{\sum_{i=1}^n \ln X_i}\)
3
\(-\frac{n-1}{\sum_{i=1}^n \ln X_i}\)
4
\(-\frac{2}{n} \sum_{i=1}^n \ln X_i\)