<p>Suppose $X_{1},X_{2},...,X_{n}$ is a random sample of size $n$ taken from a population with mean $\mu$ and variance $\sigma^{2}$. If $\bar{X}$ is the sample mean, show that $\mathrm{E}(\bar{X})=\mu$ and $\mathrm{Var}(\bar{X})=\frac{\sigma^{2}}{n}$.</p>

Suppose $X_{1},X_{2},...,X_{n}$ is a random sample of size $n$ taken from a population with mean $\mu$ and variance $\sigma^{2}$. If $\bar{X}$ is the sample mean, show that $\mathrm{E}(\bar{X})=\mu$ and $\mathrm{Var}(\bar{X})=\frac{\sigma^{2}}{n}$.

Deriving Expectation and Variance of the Sample Mean

Deriving Expectation and Variance of the Sample Mean

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