If $\displaystyle X_1,X_2,....... X_n $constitute a random sample from an infinite population with mean $\displaystyle \mu$ and variance $\displaystyle \sigma^2$, obtain $\displaystyle E[\bar x]$ and $\displaystyle Var(\bar x)$
You don't make it clear whether or not a derivation is required. So I will just refer you to a website that has the standard results which are the answers to your questions: Sampling distribution - Wikipedia, the free encyclopedia