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E[g(X)]≠g[E(X)]E[g(X)] \neq g[E(X)]E[g(X)]=g[E(X)] (except for linear functions)
aE(X)+baE(X) + baE(X)+b
a2Var(X)a^2\text{Var}(X)a2Var(X)
It only shifts PDF horizontally, not spread
Multiplies mean by aaa
Adds bbb to mean
f(x−b)f(x - b)f(x−b)
1af(xa)\frac{1}{a}f\left(\frac{x}{a}\right)a1f(ax)
1af(x−ba)\frac{1}{a}f\left(\frac{x-b}{a}\right)a1f(ax−b)
To preserve total area under curve = 1
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