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

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Alan Sherman

Answered question

2022-09-26

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

Answer & Explanation

ahem37

Beginner2022-09-27Added 15 answers

Explanation:
intuitively 0 variance using sum square difference is

(x - μ)^{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 = μ \to (x - μ)^{2} = 0

x > μ \to (x - μ)^{2} > 0

x < μ \to (x - μ)^{2} > 0

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