Proof that Variance is Non-Negative


Show that variance is never negative.

There’s 2 ways to do this: the right way and overkill.

The Right Way

Notice that you’re taking the mean of a real-valued function squared, which is never negative. Therefore, the mean can’t be negative.

The Way That It Actually Went Down

Jensen’s Inequality.

The square function is convex. Therefore, by Jensen’s inequality, the positive term in the last expression dominates the negative one, proving the statement.

This is way overkill for something that can be figured out without even writing something down.

Hindsight is rather insulting.

Related Posts

How I feel about ebooks

List of places where the US has been involved in regime change, with multiplicity

Accuracy vs Precision

Handy command line benchmarking tool

Stan Rogers

Ultimate Hot Couch Guy

Quote on Java Generics

The Programmer Tendency

Figure out undocumented JSON with gron

Mental Model of Dental Hygiene