Q45Single correct3 Marks24 Mar 2024

Let $X_1, X_2, \ldots, X_{100}$ be i.i.d. samples with mean $150$ and variance $100$. Find the mean and variance of $\bar{X}$, where $\bar{X}=\frac{X_1+X_2+\cdots+X_{100}}{100}$ is the sample mean.

A

$E[\bar{X}]=150,\ \mathrm{Var}(\bar{X})=100$

B

$E[\bar{X}]=150,\ \mathrm{Var}(\bar{X})=10$

C

$E[\bar{X}]=150,\ \mathrm{Var}(\bar{X})=1$

D

$E[\bar{X}]=1500,\ \mathrm{Var}(\bar{X})=10$