Q29Multiple correct3 Marks24 Dec 2023

Let $X_1, X_2, \dots, X_n$ be i.i.d. samples from a distribution with an unknown mean $\mu$ and standard deviation 4. Let $\hat{\mu} = \frac{X_1 + X_4}{2}$ be an estimator of $\mu$. Which of the following option(s) is(are) correct?

A

$\hat{\mu}$ is a biased estimator of $\mu$.

B

$\text{Risk}(\hat{\mu}, \mu)$ is same not as $\text{Var}(\hat{\mu})$.

C

$\hat{\mu}$ is an unbiased estimator of $\mu$.

D

$\text{Risk}(\hat{\mu}, \mu)$ is same as $\text{Var}(\hat{\mu})$.