I am trying to detemine if the expression below is concave or convex using operations that preserve convexity http://web.stanford.edu/class/ee364a/lectures/functions.pdf.
$Var[x] = E(x^2) - E(x)^2$
- $E(x)$ is concave / convex because it is a sum of linear terms
- $E(x)^2$ is convex because of power 2
- $E(x^2)$ is concave / convex because it still is a sum of linear terms.
Would this be correct ? So then what would $E(x^2) - E(x)^2$ be since it is convex - affine ?