An unbiased [[estimator]] of $\mu$ is denoted $\bar{X}$ where $\bar{X} = \frac{1}{n} \displaystyle \sum_{k=1}^n X_k$ Any estimator, including the sample mean $\bar{X}$ is a random variable (since it is based on a random sample). This means that $\bar{X}$ has a distribution of its own, which is referred to as the **sampling distribution of the sample mean**. This [[sampling distribution]] depends on - the sample size $n$ - the population distribution of the $X_i$ - the method of sampling. From the [[Weak Law of Large Numbers]], we know that $E(\bar{X}) = \mu$ and $V(\bar{X}) = \frac{\sigma^2}{n}$. From the [[Central Limit Theorem]], we know that the sample distribution approximates the normal distribution as $n$ approaches infinity.