For the following two functions $p(x,y)$, check whether $p$ is a joint density function. Assume $p(x,y)=0$ outside the region $R$.

(a) $p(x,y)=1$, where $R$ is $1 \le x \le 1.5, 2 \le y \le 4$.
$p(x,y)$ ? is a joint density function is not a joint density function

(b) $p(x,y)=2$, where $R$ is $-1 \le x \le 1, 0 \le y \le 1$.
$p(x,y)$ ? is a joint density function is not a joint density function

Then, for the region $R$ given by $0 \le x \le 3, 2 \le y \le 6$, what constant function $p(x,y)$ is a joint density function?
$p(x,y) =$