Q20Single correct3 Marks1 Sep 2024

Let $X_1, X_2, \ldots, X_n \sim \text{iid Exp}(\lambda)$, and let $\bar{X}$ and $S^2$ be the sample mean and sample variance, respectively. Select the correct options from the following:

A

Both $\bar{X}$ and $S^2$ are biased estimators of $\lambda$.

B

Both $\bar{X}$ and $S^2$ are unbiased estimators of $\lambda$.

C

$\bar{X}$ is an unbiased estimator of $\lambda$ while $S^2$ is a biased estimator of $\lambda$.

D

$S^2$ is an unbiased estimator of $\lambda$ while $\bar{X}$ is a biased estimator of $\lambda$.