Let $X$ be a random variable with probability density function

$$f(x) = \left\{ \begin{array}{ll} c(3 x-x^2) & \mbox{if \ } 0<x<3 \cr 0 & \mbox{otherwise} \end{array} \right.$$ Find the value of $c$: $c =$

Find the cumulative distribution function of $X$:

$F(x)=$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right\lbrace$ if $x\le 0$ if $0<x< 3$ if $x\ge 3$