Let $p(x,y) = 1 x + \frac1{4}\, (y + c)$ on the region $R$ given by $0 \le x \le x_1$ ($x_1 > 0$), $-2 \le y \le 2$, with $p(x,y)=0$ outside the region $R$.

(a) For what values of $c$ can $p$ be a joint density function no matter what $x_1$ is?
$c$ ? > >= < <=

(b) Next, take $c$ to be the endpoint of your inequality in (a). Find a value of $x_1$ for which $p(x,y)$ is a joint density function.
$x_1 =$