# What is the distribution of $\bar x$?

Let $x_1,x_2,\ldots,x_n$ be a random sample from a normal distribution with mean $\mu$ and and variance $\sigma^2$. show that $E[\bar x]=\mu$ and $V[\bar x]=\sigma^2 /n$, where $\bar x = \frac1n\sum_i x_i$ is the arithmetic mean of the $x_i$.

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Also what is the distribution of xbar –  david Apr 4 '13 at 16:54

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