# Why Estimation Theory

In statistics, we work with samples. For example, the sample mean is easily calculated. However, it is the population mean that is more valuable.

Suppose we have one sample $S_i$, which is used to calculate the mean of the sample $\mu_i$. We have two key problems to solve at this moment.

- Can we use this sample mean $\mu_i$ to represent the population mean $\mu_p$?
- How good is our estimations?

To answer these questions, we need to work out the properties of the samples themselves and work out a theory to instruct us to infer population statistics from sample statistics.