Unbiased Estimator for Location Parameter in Shifted Exponential| UPSC ISS 2025 Paper-2 | Problem-25

Описание: This video derives an unbiased estimator for the location parameter \(\theta\) when sampling from a shifted exponential distribution with PDF
\[
f(x) = e^{-(x - \theta)}, \quad x \theta,
\]
which is an exponential distribution shifted by \(\theta\). Using the sample mean \(\bar{X}\), the unbiased estimator for \(\theta\) is found as \(\bar{X} - 1\), since the expectation of \(\bar{X}\) is \(\theta + 1\). A clear, practical example of estimator construction with shifted distributions.

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