I am trying to understand estimator bias and was a little perplexed by this example.src)
$$ \mathbb{E}[\overline{x}] = \mathbb{E}\left[\frac{1}{N}\sum_{i=1}^{N}x_i\right]=\frac{1}{N}\sum_{i=1}^{N}\mathbb{E}[x]=\frac{1}{N}\cdot N\cdot\mathbb{E}[x]=\mathbb{E}[x]=\mu. $$
Why does $\sum^m_{i=1}\mathbb{E}[x_i] = m\mu$? No explanation was given other than the fact that the data samples $\{ x_1,x_2,\dots,x_m\}$ are i.i.d.