Hands-On Mathematics for Deep Learning

Variance

We define the variance of X as follows:

The standard deviation of X is the square root of the variance:

We can think of this as how spread out or close values are from the expected (mean) value. If they are highly dispersed, then they have a high variance, but if they are grouped together, then they have a low variance.

Here are some properties for variance that are important to remember:

• _.
• If , then _.
• _.
• _.
• , given that all the X