Chapter 15.10, Problem 2P

Let $x_1,x_2,\cdots ,x_n$ be independent random variables, each with density function $f(x)$, expected value $\mu ,$ and variance ${\sigma }^2.$ Define the sample mean by $\bar{x}={\displaystyle \underset{i=1}{\overset{n}{\sum }}{x}_i}.$ Show that .