Q1Single correct3 Marks10 May 2026

Suppose $X_1, X_2, \dots, X_{100}$ are i.i.d random variables with $E[X_i] = \mu$ and $Var(X_i) = \sigma^2$ for $i=1,2,\dots,100$. Let $\hat{\mu} = \frac{1}{90}\sum_{i=11}^{100}X_i$ be an estimator of $\mu$. Find the mean squared error (MSE) of $\hat{\mu}$.

A

$\frac{\sigma^2}{90}$

B

$\frac{\sigma^2}{90^2}$

C

$\frac{\sigma^2}{100}$

D

$\sigma^2$