Question

What is the lower bound of a random variable's variance?

Answer 1

`0`

Explanation:

intuitively `0`

variance using sum square difference is `(x-mu)^2`. There are of course other choices but generally the end result will not be negative. In general the lowest possible value is 0 because if `x=mu rightarrow (x-mu)^2 = 0`
`x>mu rightarrow (x-mu)^2>0`
`x< mu rightarrow (x-mu)^2>0`