Solution
= Solution
The <probability density function> is the <derivative> of the <cumulative distribution function>:
$$
\boxed{f(x)=\begin{cases}12x^2(1-x),&0\leq x\leq1,\\0,&x<0\text{ or }x>1.\end{cases}}
$$
It is nonnegative and has <integral> $F(1)-F(0)=1$. This is a <beta distribution> with parameters $3$ and $2$.