Solution
= Solution
The <expected value> is
$$
\mathbb E[X]=\int_0^1x\,12x^2(1-x)\,dx=12\left(\frac14-\frac15\right)=\frac35.
$$
The second moment is $\mathbb E[X^2]=12(1/5-1/6)=2/5$. Hence the <variance> and <standard deviation> are
$$
\operatorname{Var}(X)=\frac25-\left(\frac35\right)^2=\frac1{25},\qquad\boxed{\mathbb E[X]=\frac35,\quad\sigma=\frac15.}
$$