Properties of Mean and Variance (VCE SSCE Mathematical Methods): Flashcards

$E[g(X)] \neq g[E(X)]$ (except for linear functions)

$aE(X) + b$

$a^2\text{Var}(X)$

It only shifts PDF horizontally, not spread

Multiplies mean by $a$

Adds $b$ to mean

$f(x - b)$

$\frac{1}{a}f\left(\frac{x}{a}\right)$

$\frac{1}{a}f\left(\frac{x-b}{a}\right)$

To preserve total area under curve = 1