A joint density function is given by $$f(x,y)= \begin{cases} kx^{2}\quad&\mbox{for } 0\le x\le 3 \mbox{ and } 0\le y\le 2, \\ 0&\mbox{ otherwise.} \end{cases}$$ (a) Find the value of the constant $k$.
$k =$

(b) Find the probability that $(x,y)$ satisfies $x+y\le 3$.
probability =

(c) Find the probability that $(x,y)$ satisfies $x\le 1.5$ and $y\le 1$.
probability =