Normalizing inputs (part 2)

The video contains a typo:
If X has mean $\mu$  and variance $\sigma^2$ , then $Z=(X-\mu)/\sigma$  has mean $0$  and variance $1$ . That is, to normalize $X$  we should divide by the standard deviation $\sigma$  (not the variance $\sigma^2$  as stated in the video). 

We can verify the values of the mean and variance of $Z$ :

• $\mathbb{E}[Z]=\mathbb{E}\left[\frac{X-\mu}{\sigma}\right] = \frac{\mu-\mu}{\sigma}=0$  
• $\mathbb{E}[(Z-0)^2] = \mathbb{E}\left[\frac{(X-\mu)^2}{\sigma^2}\right]=1$ .